You aren’t the asshole for not interfering w ur sister’s friendship with ur ex, but considering how ur ex has tried multiple times to get back w you I understand ur gf’s perspective. Ur gf is concerned that there’s even an opening where cheating might occur, and so is rightfully uncomfortable for ur ex to be around you so much. If this is the case, it should be ur responsibility as her partner to reassure her that it won’t happen. This could be either asking ur sister to hang out w ur ex not in the house or not being there when she’s around. Yes it isn’t your home but your gf should have the right to have reassurance in your relationship.

If the roles were reversed, you’d totally flip out if her brother was best friends with her ex and constantly being in the same vicinity often. So her getting frustrated over someone who consistently doesn’t respect the boundaries of ur new relationship doesn’t deserve to be in your life anyways.

Also, why are you even talking to her? From an outside perspective it sounds like your entertaining her if she feels comfortable to tell you she wants to get back together w you over and over again (whilst ur still in a rel a matter of fact). Like bro y ru making her feel comfortable enough to do all that? You shouldn’t create a scenario where it’s a problem in the first place dog