At the start of the game, Josy and Maya were all but broken up - they were split with only the slim prospect of Josy getting into B&R as a "reject" to offer them a chance of even being in the same room at some point, and even then they'd be under constant strain trying to keep Patrick (who has access to roam campus, and a key to Maya's dorm room) from discovering they were trying to keep a relationship going. Josy was on the verge of running away to try to start a new life somewhere else, and Maya was desperately hoping to find some way to get some degree of independence from Patrick.
For both of them, the relationship was all but over, and Tremolo offered something to both of them - for Josy, he's someone who would be willing to be openly dating her without all the secrets and lies that have been strangling her relationship with Maya; for Maya, he's someone she wouldn't have to hide from Patrick.
Then Josy gets in, and gets assigned to the "empty" bed in Maya's dorm room and everything turns upside down.
Josy and Maya then have very different experiences with and perspectives on the HOTs - Josy meets a welcoming group of potential sisters with one asshole; Maya meets a manipulative bitch who dangles the prospect of solving her problems in front of her, only to deny it was ever a possibility, and the people who happily spend time with her. And then it's made clear that Quinn way over-stepped with Josy and Maya's hazing, with no immediate consequences. So Maya's seeing a group of people represented by Quinn, while Josy sees Quinn as an exception to the sisterhood.
On top of that, Josy's not stupid - she can see that sharing a room with Maya means it's only a matter of time before Patrick catches them - so of course she's willing to put up with Quinn in order to be a member of the HOTs and move out of Maya's room. And of course Maya doesn't want anything to do with Quinn and the people who enable and support her.
To Maya's credit, once she actually interacts with individual non-Quinn HOTs, she realises she's misjudged them, and she does, ultimately, come around (and credit to Sage and the HOTs for fixing Quinn's fuck-up there rather than taking Maya's rejection as a sign she's not the right sort to join them).
With or without Tremolo in the mix, the Josy/Maya relationship is still under a lot of strain - Maya is (not unreasonably) unwilling to risk her entire future by coming out as a lesbian when there's any risk of Patrick finding out, while Josy wants a girlfriend whose hand she can hold when she wants to show affection. So long as Maya is afraid of Patrick being able to nuke her life, the relationship's never going to be easy. It's going to be up to Josy and Maya whether the relationship is worth the work needed to keep it going, though Tremolo can nudge the decision either way (and does in the non-throuple chapter 9).
There's an easy path to a breakup - either Maya's financial issues are finally resolved, but she's still not willing to go public with Josy, and Josy loses patience (with Tremolo there to help them reconcile, or to drive the wedge deeper) or Maya's financial issues remain, with no prospect of ever being resolved, and Josy loses patience.
There's also the prospect of Patrick being won over somehow - if his biggest issue with Maya being a lesbian is the lack of grandkids, the prospect of them (particularly if Maya gets pregnant somehow) is likely to soften his position. He's abusive and controlling, but at least part of that comes from his being under a lot of stress himself, and he's not necessarily totally unreasonable.
As for Josy's non-Maya drama, that seems to come down to her being a teenager and treating all the adults in her life like they're against her just because they don't give her total autonomy. It seems like they've got her back, even if they did confiscate her phone when they caught her having sex in her parents' bed...