Really sorry you are having such a hard time at the moment
I'm sure it's not that your parents don't care about you staying away, but they are probably upset by the rows and have no idea how to resolve things without upsetting either you or your brother. How often is his girlfriend there, could you try to visit when she's not around?
Obviously don't answer this if you'd rather not, but what sort of things do you and your brother's gf row about? Is there no way of calling a truce and at least being polite to one another even if you don't really like each other for the rest of the family's sake? Where's your brother in all this, could he talk to her and get her to be more reasonable?
It's such a shame if you don't feel able to attend a family celebration just because she's going to be there. I think you should go, avoid brother's gf as much as possible, be cheerful and scrupulously polite to her if you have to have contact and if she's unpleasant just walk away, then if there's any 'atmosphere' it will be obvious who's generating it and perhaps she won't get asked next time. I know it's easier said than done though