My mother has developed certain behaviors that my fiance says do not bother him, such as going to the kitchen and watching what he is doing like washing dishes or fixing something to eat. He calls her a nuisance. I agree she may do these things but she has done them before the dementia developed. Maybe I should have thicker skin, but it bothers me when he says these things to me because she still is my mother. This then results in conflict and hurt feelings. I just want support not criticism of my mother's habits.
I too was a little put off by your description of how your fiancee is behaving. Coming to you in private and talking with you about how your mom can get on his nerves is one thing. It's respectful of your feelings and it's respectful towards your mom but calling her names ("nuisance") to you, her daughter, is not a nice or appropriate way of dealing with his feelings. It's a cheap shot at someone who is vulnerable (your mom) and it puts you in an awkward position (either having to defend your mom or validating his feelings which could just reinforce his behavior).
Have you told him that you need his support? If not, do. Have you explained to him that his attitude towards your mom puts you on the defensive and that you do not want to have to choose who to support, him or her?
If you have had these discussions and his behavior has not changed then it probably never will.
Partners in life support one another. He should be helping you care for your mom, not insulting her and by extension, you.
Is this his house, or yours together? That will tell something as well.
Living with someone who has dementia is hard, so maybe we should cut him some slack. I suggest trying a few sessions of relationship counseling to sort this out.
He has a right to his feelings, just as you do. He finds your mother's behavior a nuisance. He's not entitled to be abusive to her, but he is entitled to complain. But only a little! Is he good to her in other ways?
I suggest that when he complains, you sigh, and agree with him that it's annoying, because it probably is. Let him talk for a short time, them remind him that she doesn't do it to annoy him, but can't really help it. If you acknowledge his feelings, he might be able to stop there.
If he needs or wants to vent long and/or loud, you have a right to tell him that it's hard for you to listen to, and can he find someone else to talk to at length. If he's being mean to her face, of course, that's not OK. But he has a right not to like the situation and to say so briefly from time to time. He has a right to see you taking his side part of the time. If you can be sympathetic to that, hopefully he will be able to express his frustration and let it go.
Hang in there!