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Legal's Mate or Legal's Trap is a chess checkmate pattern that ends the game with a queen sacrifice.
Hera didn't switch Percy Jackson and Jason Grace.
Instead, she switched Annabeth Chase and Reyna Avila Ramirez-Arellano.
So Reyna wakes up in the bus headed to the grand canyon without her memory, and she's confused why she has a dagger and a spear with her and why Piper and Leo act like they know her.
Also, Hera doesn't magically make anyone fall in love with Reyna because that's messed up and maybe she found out that Reyna was aroace when erasing her memories.
Or Hera does make either Piper or Leo fall in love with Reyna, making her realize her asexuality and the uncomfy situation earlier than Piper and Jason did. I'm not writing the story, so it's up to you now.
If it's Piper, then the whole memory wipe thing is also her bi/lesbian awakening along with Reyna's aroace awakening. If it's Leo, then we can get some Leo angst when Reyna lets him down slowly that she's not into him or anyone else for that matter.
When Dylan attacks, Reyna's quick on the update despite her lack of memory and either seriously wounds him or kills him with a throw of her spear, and no one falls into the grand canyon which is good because none of them can fly. Oh, and Coach Hedge didn't get kidnapped.
Percy shows up with Butch and he's really frantic about Annabeth's disappearance. It's like when she got kidnapped during the Titan's Curse, but worse, because there's zero clues and Percy's PTSD-ridden imagination is going wild thinking of all the different things that could've happened to her.
Reyna thinks Percy looks familiar, but she doesn't really know why, other than an odd sense of foreboding. She remembers that she's a demigod of Bellona, but no one's heard of her other than Chiron, since her Greek form is Enyo and no one really knows about her either.
The quest to save Hera mostly goes the same, though with a lot more guessing and close calls since Reyna can't fly. Coach Hedge is still here because he wanted to go beat up those venti that bested him before. He's kind of needed to help Tristan McLean when they find him.
When they meet the Hunters of Artemis, Reyna looked at Thalia and said that her eyes reminded her of Jason. Thalia freaked out, of course, because what do you mean, amnesiac mystery demigod knows her supposedly dead brother?
So they talk about Jason and Wolf House and Leo realizes earlier that Reyna and Annabeth must've been switched between the Greek and Roman camps, so nothing bad happened when he got excited and set himself on fire.
Thalia's excited that her brother might be alive, of course, and she asked Reyna if she remembered anything else, but Reyna really couldn't. She thought that she might be in love with him, but the way she said it made it sound more like she was just doing it because it was expected of her with all the urgency of ticking an item off of a checklist, and the Hunters notice. So Reyna gets some aroace girls explaining the option of being aromantic to her and Reyna feels a connection with them that may lead her to joining the Hunters later, but not right this instant.
Thalia goes with the others when they talk to Aeolus since Leo didn't melt the bridge, and Reyna is very respectful toward the harried god. Unfortunately, he still tries to get them killed and they fall off the island, but Thalia panics because fear of heights and all that and accidentally powers up her latent flying powers through fear and adrenaline and saves them all.
Reyna prays for her mother's help while they're fighting Enceladus, and Bellona gives the group her blessing which allows them to slay the giant.
They rescue Hera just like in canon, although this time no one dies from seeing Hera's true form because Reyna was faster than Jason at closing her eyes.
Annabeth wasn't forced to sleep for how many months unlike Percy, since Hera correctly deduced that as a child of Athena, the Romans would need some more time to get used to her. It's different than being a child of Neptune, since they just didn't respect him, but Minerva's a virgin goddess and doesn't have any demigod children.
Well, until Savannah, but I really don't know what's up with her. What do you mean, she's a legacy of Minerva?
Maybe Minerva had a random kid and never claimed them until after the giant war? I have no idea what's going on here.
So Annabeth goes to Camp Jupiter and meets Frank, Hazel, and Jason, who are all looking for Reyna. Jason reminds Annabeth of Thalia, and something about that name sparks Jason's memory, but Jason was two when he was abandoned and Annabeth's got amnesia and can only remember Percy, so they don't really go anywhere.
Annabeth keeps insisting that she's a daughter of Athena, despite everyone's skepticism, and it leads to an awkward conversation where Annabeth explains how her mom has mind sex with people while Annabeth herself has amnesia and doesn't really remember stuff. Although she's still insanely smart, and that combined with her sureness that she's a child of Athena, not Minerva, leads to everyone realizing that she's Greek.
Octavian freaks out, of course, but Jason decides to trust Annabeth and so she joins the fifth cohort, slowly gaining the trust of the rest of the Romans. Annabeth uses her strategies at capture the flag to help the cohort win the war games, and she learns all she can about Roman history, although Octavian keeps trying to stop her since he's still a bit worried that she might be a very clever Greek spy sent to destroy the camp. Annabeth's a big fan of New Rome University for obvious reasons, and wonders if she could build a life here with Percy.
Also, Octavian gets character development. He and Annabeth don't like each other, but they slowly get a grudging slight respect, at least. It develops extremely slowly while Octavian keeps shadowing Annabeth trying to see if she's up to something. Eventually, he figures out that Annabeth is legitimately just suffering amnesia and has no idea why she's here other than godly intervention, and that she might actually be trustworthy and not about to backstab them.
If this sounds too reasonable to be Octavian to you, then that's your opinion. Seriously, Octavian's just trying to make sure New Rome's safe, but everyone hates him way more than Luke 'war crimes' Castellan. Probably because being annoying is worse than a war crime in most people's opinion.
Annabeth keeps trying to regain her memories, and eventually Nico shows up, and Annabeth thinks she recognizes him. Nico lies about it, because last time there was a prophecy and someone got their memories wiped by a god (him and Bianca), the gods almost got overthrown, so excuse him for not trying to get in the way of the Fates. But Annabeth deduced that he's not telling her something, and eventually Nico just spills what he knows about her.
But by that point, Thanatos has gotten captured again, and Mars shows up with a prophecy and quest that Annabeth, Frank, and Hazel undertake. They run into Stheno and Euryale, and the three of them kill the gorgons and get vials of poison.
When they run into Phineas, however, Annabeth doesn't bet with the vials. Instead, she challenges him to a game.
By the way, Annabeth's been pretending to be a Roman demigod that isn't Minerva since she thought it would be more strategically sound that way, so Phineas doesn't know about her true parentage.
Phineas writes the answer on a sheet of paper that he then sits on, and Annabeth beats him at whatever strategic game they agreed upon. Phineas of course then tries to get rid of the paper, but Frank had his bow out and shot him into dust, so they still know where to go and still have the vials of gorgon blood for just in case.
By the way, throughout the whole quest, Annabeth's been getting confusing visions from Athena/Minerva, saying stuff about getting the Athena Parthenos, but that really only gets understood after this quest is over.
Her invisibility cap probably stops working since Athena sees her daughter on the Roman side.
Then the group runs into the Amazons, who are in a tizzy since Hylla heard about her sister's disappearance and is worried about her. Some angst about failing to keep in touch with Reyna and now she's gone and they might not see each other again. Hylla also recognized Annabeth as the one who released Blackbeard, and while Annabeth doesn't really recognize her back, she has enough context clues to figure out what's wrong.
At Hubbard glacier, Annabeth comes up with a plan involving Hazel summoning imperial gold weapons, which are explosive, and setting off a chain reaction that takes out most if not all of the enemies. Then Arion drags Alcyoneus to Canada and they defeat him.
The three of them are more banged up than in canon, of course, since Annabeth can't summon a hurricane, but they're alive and they have the golden eagle thingy, so it's okay.
Annabeth may have gotten seriously hurt during the fight, but she drank the gorgon's blood that healed her. And she knows which one it is because she tested a bit on a stray bird that they found on the quest.
Drinking the gorgon's blood also brings her memories back, though that doesn't really kick in until after the battle with Polybotes.
Speaking of that, Annabeth defeats him by throwing the deadly vial of gorgon blood at him while Terminus distracted the giant with his antics, technically fulfilling the bit where giants can only be killed by gods and demigods working together.
Annabeth gets named praetor in Reyna's absence, and she gets a dream about the Argo II coming to Camp Jupiter. Octavian rolls his eyes and mutters something about how of course there's going to be more Greeks the instant he gets used to the first one, and something about how they'd better behave while on Roman soil.
Terminus throws a fit about no weapons inside the Pomerian Line when the Greeks arrive, but Annabeth, who's well used to him by this point, points out that there's no rule about flying ships hovering over New Rome.
Percy, who still has the Curse of Achilles since he came to New Rome on a flying ship instead of wading through a river, finally reunites with Annabeth, and there's no judo flipping to interrupt it this time.
Reyna also reunites with Jason, but it ends less happy than the other reunion, since Reyna's character development involved loosening up and relaxing as well as figuring out her aroace self, so she kind of broke up with him. Does it count as breaking up if they hadn't really started dating yet in the first place?
Octavian watches everyone meticulously, but it's not as dogged as when Annabeth first showed up. He kills someone's stuffed animal to check the future, just in case.
The eidolons still possess Leo and fire on New Rome, but Percy harmlessly takes care of Leo and disarms everyone without seriously hurting them, also kind of proving that if the Greeks really wanted to fight the Romans, Percy could probably handle them all by himself. He did beat gods before, and he didn't even need the curse to best Ares.
Octavian's extra suspicious now, of course, but Piper gets the eidolons to leave Leo and everyone agrees that if Gaea's trying to split the Romans and the Greeks up, then that means they absolutely have to team up. Besides, they trust Annabeth, and if Annabeth says the Greeks are okay, then they're okay.
Octavian's still grumpy about it, of course, but he's not starting a war or anything.
So the next stations of the canon get taken care of by the Greeks and Romans working together, more or less splitting up the troops a bit to try rescue Nico, find Bacchus, and defeat Ephialtes and Otis.
Meanwhile, Annabeth starts trying to find the Athena Parthenos.
She still falls into Tartarus with Percy, but the Tartarus trip goes better considering Percy's still basically invincible.
Also, the River Styx flows into Tartarus, which gives Annabeth an idea.
If Percy can be invincible, why can't she?
Though I'm pretty sure a curse from an arai will still hurt even with the Curse of Achilles.
Back on the surface, the Romans are helping the Greeks transport the Athena Parthenos, and eventually reunite with Percy and Annabeth. The most important parts after this happen pretty much the same, other than the fact that there's no Greek-Roman war.
The two camps fight against Gaea and Leo sacrifices himself, but we all know he'll be back. Octavian also doesn't die since he doesn't get stuck to a firing onager.
Reyna retires from being a praetor and joins the Hunters. Jason may or may not see what the Greek camp is like as he personally finds Camp Jupiter rather hidebound, and he reunites with Thalia and maybe steps down as praetor as well since he never really wanted to lead. Frank and Hazel become their successors, as Annabeth, who's also technically praetor, just wants to relax and go to college.
Yeah, they'll totally get to do that. It's not like Apollo's going to fall out of the sky, rendered completely mortal or something.