Well, I'm not sure that Mom moving in with a boyfriend is petty and small.
Granted, it's something that NCP can't control (unless there's a no paramour order), but it is a significant event in the child's life and has major repercussions - both logistical and moral. CP ought to (out of courtesy, if nothing else) discuss it with NCP - and maybe give them a chance to meet. I'd certainly want to meet someone who's going to be living with my daughter.
Of course you would Misto...as would most parents.
However, in this scenario dad is remarried and while the child is with him, the child is living with another adult in the household. Now granted, dad got married rather than shacking up, but we don't know that dad didn't live with stepmom for a period of time prior to getting married.
The reality of things is that separated/divorced parents do usually move on and what is sauce for the goose is also sauce for the gander. If mom must accept a new significant other in dad's life, then dad must also be prepared to accept a new significant other in mom's life.
Unfortunately, no matter what the gender of the parent, there are frequent instances where the other parent is simply not prepared to accept their child's parent moving on into a serious relationship...even if they are in one themselves.