So I need some advice/opinions

My mom and my fiance' don't get along real well. I mean alot of times they "compromise" to get along I guess, but Everytime a argument happens they both hold on to it.. my fiance doesn't necessarily like my mom because he thinks she favorites our oldest child more than the two younger ones which I have to say myself that she kinda does, she doesn't think she does but it's noticeable. Like for example if we ask her to watch the kids for the day or whatever she will say she can keep the oldest one but not the other two because the middle one "gets into everything" (he's 18 months so yeah he probably does but he doesn't know any better 🤷)

Also if the middle child and oldest child is doing something they shouldn't be doing she will be more hateful towards the middle child instead of the older one. And a few more things. So that's why he has a problem with her.

Apparently she has a few problems with him, for one she claims that he favorites the middle child more than the others, she always gives him weird looks even if he's not talking to her, she thinks he babies the middle child to much, which I will say yeah he probably does show alittle more compassion cause he's always the one getting "hurt" and that's his excuse, so they BOTH make excuses for there actions. And in general she just don't like him. They constantly have something negative to say about each other. Personally I don't favorite any of the kids, I treat them all the same. But I feel like they will never see eye to eye when it comes to the kids.. and of course I'm put in the middle of it Everytime .. I don't see why everybody just can't keep there mouth shut and get along, I feel like I'm eventually gonna have to choose either my fiance or my family because it's going to be a on going thing it seems like. I'm just confused about it all. They are both so stubborn so even when I'm the one who steps up and tries to sort the problem out neither of them wants to admit to there faults. I don't wanna have to choose. Any opinions or advice ??

Please no negative comments towards me. It's not my fault they are like this, it ain't me doing it, it's them.. I'm trying to figure out how to fix this problem before it gets worse.