It's the hardest situation in life. You know, your wife gives you sex, even if not as much as you'd like, and you obviously love your kids, and she's threatening to take it all away. That's tough.
I miss my daughter like crazy. And I miss having sex with my wife. But she wanted her parents to live in our house forever, even taking them on vacations. And because they are hispanic, they'd be talking spanish in the house among themselves.
If you allow her mother to stay, that gnaw in the pit of your stomach will just get worse. She clearly doesn't respect you, because if she did then she'd value your home and space and boundaries. Check out some of the content on the YT channel redonkulus.