I think it's a deal breaker, as you say "I had three children when we met, I still have three children" My husband had two children from a first marriage when we got together 37 or so years ago, I've been lucky in my relationship with them, and the grandchildren that have come along. I know that is not always the case, nevertheless they were there first. They can't just go away and it's a fact, adult children do boomerang back to the family home for various reasons, I had those two children stay with us from time to time before they established their own homes and then our own two have been backwards and forwards at different times also. I a have our own fairly young grandchildren stay every other week end so I know what it's like to have your home taken over, but I also find there's a heightened sense of pleasure when peace and calm is restored.
Your son, as you describe him, doesn't sound too much trouble of course it's important adult children clear up after themselves, all that needs to be ironed out and as a courtesy, try and agree Christmas arrangements and overnight stays with your other half beforehand. However, if she won't countenance any visits, then I'd say you're stuffed and you have to put it to her your ongoing relationship with them is non negotiable. I see you have been together 7 years, so she must have been used to them being around in the first place but it seems she is increasingly losing her rag of late, I think you need in depth discussions around that. I would put it to her "don't make me choose because, as a mother I will choose them" . You don't say whether she is a parent herself, if not, she may not fully appreciate the mother/child bond. The last thing you want is to end up estranged from your children it will be a massive source of resentment and could quite possibly ruin your relationship with her anyway.
Sometimes 2nd time around relationships with baggage work better when each party has their own home and can retreat there alone in times of stress. I think that's the only workable scenario for some with adult children. I do know one couple who have managed to keep their relationship going very well but with separate homes and exclusive times with their own grown up children and grandchildren without melding the whole lot together. That works for them. Horses for courses and all that!
I wish you all the best in sorting this considerable dilemma out.