Being petty about MIL??

So my fiancé and I rent a 3 bed room apartment for the both of us, our son, cat, and 2 dogs.. Recently his mother and little sister moved in with their untrained kitten and 2 birds. She works most days but just goes to her room (which was our room- the master bedroom) when she gets back and doesn't come out until she has to go to work the next day or unless she has to go shopping or something. His little sister stays in his moms room all day playing on her phone or video calling her boyfriend. (She's "homeschooled".. meaning she doesn't go to public school but also doesn't do actual online or home schooling). My fiancé and I are the ones who clean. If we don't, they don't.. They wouldn't anyways. They seriously have to be told that their room stinks and to do laundry or to clean up after themselves. They let the kitten run around the apartment unsupervised, which means it pees and poops in our fucking apartment (and they aren't trying to potty train it). It's either my fiancé or myself that has to clean up after it. They don't feed/water/clean up after the kitten or their birds. We've already got enough going on with taking care of our month old baby, and taking our pup & dog out.. Sometimes we will ask his mother to watch the baby while we go to the store or a doctors appointment, but that's hardly ever, and when she does watch him she will let him sit in his wet/dirty diapers. Sure, we aren't ever gone for more than 1 1/2 to 2 hours at the most, but since she's "raised kids before" she should fucking know to change his diaper. (And she's hardly raised her own children btw, my fiancé was the one who did it for her. He dropped out of school to raise her 3 other kids because she wasn't there). I've also noticed that she will take off his mitts and let him "play" with things that have been on the floor or near dirty dog toys, and she's taken off his socks I've put on him and puts mismatched socks on him. When she feeds him she doesnt burp him so when he gets laid down he ends up spitting up and even throwing up, and he's choked a couple times. I've actually told my fiancé that I don't want her feeding him because she fails to burp him every. single. time. and I don't like her watching him because 9/10 times she's on her phone, not paying attention.. it's frustrating because I/we really need time to ourselves but I don't trust her with our son. Like I said, we hardly leave him with her in the first place. The only "alone time" we get is when we grocery shop or our son is sleeping.

While I appreciate the little bit of help with bills, we aren't in a situation where its needed, I feel like a live-in maid, and I really just don't like her being around our kid. My fiancé keeps saying we'll look for a different place to live, but I honestly feel like he should just tell them they need to leave, but she doesn't have good enough credit to rent her own house or apartment.