Work Text:
In one universe, Beryl Grace gives up her son Jason to Juno.
In another universe, Thalia decides to take her baby brother and leave their obviously inept mother before she does it.
So Thalia packs up whatever she thinks is important and runs with Jason in tow. Since she left much earlier, Thalia doesn't run into Luke or Annabeth, though they still meet each other.
Thalia ends up struggling after a while since taking care of a baby isn't easy, especially for a kid, but luckily, the siblings end up running into the Hunters of Artemis.
Artemis helps them, since she's a protector of maidens and children, and it's not long before Artemis asks Thalia if she'd like to join the Hunters.
Thalia says that she only will if she's allowed to take care of Jason because she doesn't trust anyone else with him.
We know that Artemis doesn't approve of boys, but Jason's two, and again, protector of children. Plus, he's Thalia's brother. Artemis would be a hypocrite to not let her Hunters be with their brothers considering Apollo. And Artemis did have male Hunters in Greek mythology, though the whole Hunters of Artemis thing was more of a Riordan thing. Artemis taught Hippolytus and Scamandrius, but she wasn't able to save Scamandrius and Hippolytus ended up getting cursed to die. Maybe the fact that having male Hunters doesn't end well is why she slowly stopped accepting them. Or how social standards make boys feel weird about swearing off of sex and romance. Or something.
But either way, Jason gets to stay with Thalia.
Also, Thalia still gets the aegis when Amaltheia shows herself to the Hunters and beckons for Thalia to follow her. The Hunters find Halcyon Green's house and kill all the monsters in there and free Hal, so he gets a happy ending.
Luke never ends up meeting Hal and the seed of mistrust in the gods never gets planted. That path fully dies once Grover finds him and Annabeth and safely delivers them both to camp since there wasn't a child of the big three to attract unwanted attention to them. This also means that there's no Thalia's tree to protect camp, but that's a later problem.
The Hunters figure out a little while later that Thalia's a daughter of Zeus and Jason's a son of Jupiter, though since Thalia's already not aging and Jason eventually joins the Hunters too once he's old enough, neither of them were eligible for the great prophecy.
Some of the Greek Hunters are also having a mild breakdown that the Roman gods exist. Some of Artemis' older Hunters are Roman and the really old ones remember when the whole Roman thing came around, but after the split, Artemis mostly stopped getting Roman Hunters and kept the other pantheon a secret. Camp Jupiter has way less interactions with the gods than Camp Half-Blood and it seems like they don't have a Hunters of Artemis or Diana over there as anything other than a legend.
Jason doesn't get sent to Camp Jupiter and stays a Hunter, because why would he? He already pledged and everything.
As it is, I don't really know where to go with this story idea so I'm putting it out for someone else. There's just too many butterfly effects to juggle. Luke never joined Kronos, Camp Half-Blood doesn't have a protective barrier but seriously why don't they what gives, Grover got his searcher's license sooner and never met Percy, Grover's probably dead by now sadly, the whole plot of Sea of Monsters is just straight up gone now, the only child of the big three eligible for the great prophecy until Bianca and Nico come along is Percy so everyone's extra focused on him, Jason doesn't die, etc.
Someone else with more time and passion can figure out where this story goes. And probably someone who's fine with killing off characters, because I really don't know how to save Grover unfortunately, which is another reason why I'm not writing this.