Wait, are A&J moving in WITH you, or just nearby? I interpreted "moving her family here" as "this city" but it appears Kevin interpreted it as "my house."
I personally recommend never making a long distance move straight into a live-in relationship. It takes time for people to adjust to just seeing each other more regularly, and putting everyone under one roof can add a lot of stress.
Compound that with J's medical problems (massive brain surgery is never a small matter) and your mental health issues (my mother and girlfriend are both BP, so I know how much strain that can put on even the healthiest of relationships), and it's a recipe for trouble.
But for all that, you sound like a reasonable person with her head on straight. Play it by ear, you might surprise yourself. Above all, communicate the shit out of everything, and don't be afraid to let yourself have your feelings. Some of them you might just deal on your own - BP often causes sensitivity to things people do unintentionally. My gf and I were actually talking about that last night. Apparently she's been hurt by me tons of times where I did absolutely nothing wrong, but her BP just made her react to something in a different way. For her, that means every time her feelings get hurt, she has to analyse them and try to figure out whether the person actually did something wrong or is it just in her head? And sometimes she'll decide that it was just in her head, but that she still needs to communicate it, but with emphasis on "this is my thing, but I just wanted you to know."
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker