I don't know why mothers are automatically assumed to be the best custodial parent.
I'd get rid of the idea that "they are boys" and so hitting is okay if it's not too hard. Stop the physical stuff now, on everyone's part! A 16 year old ought to be able to keep his hands to himself, and an 8 year old needs to stop wrestling or horsing around with someone bigger than him. Enough already. Then you can say it's not allowed in your home.
If you don't think your relationship will hold on through this drama, that's a huge consideration. Why isn't it strong enough? Is this the guy for you?
Giving in to her nonsense encourages more of it, but staying in this situation encourages more lying too. You cannot reason with her, and the courts have heard a zillion complaints like this with one party saying the kids get hurt and the other saying "She's exaggerating." She's not calling DFS, is she? Custody discussions should involve the two parties and the lawyers or mediators, not the kids. Any parent who involves the child is doing that child a disservice. My husband's ex did that, and both kids have long-lasting issues even in their early 30s.
If you move out, you're giving in to the ex. But if you don't think your relationship with your fiance will hold up, then it may not make sense to move your son into this situation, or to put your relationship under that kind of stress. If you live separately, and your fiance gets custody, there will not be anything in the agreement that says he cannot remarry. However, if you live separately, he and you are telling his children that you are secondary, and it may be difficult to establish yourself once you move back in.