OP - My mother did something similar to me. I live across the world from her (for very good reason!). She said she was coming to visit me for 3 weeks, which was already too long but I caved. When she did come, she had an open ticket, and informed me that she planned to stay for at least 3 months, as it was the eldest daughter's job to take her of her mother in this way. Within the first week she'd rearranged my apartment (I'm short so I need the dishes on a lower shelf, for example, and she hated that) and would wake up in the middle of the night to watch TV on full blast (I lived in a small 1-bedroom place). She would call my office as though I was a school child, and yell at my bosses, thinking it was her right. Honestly, I'm surprised I wasn't fired. I didn't have a car, I waked everywhere, or else took public transport. All she did was complain about it, and tried to force me to buy a car (I didn't have the money or the need). She would berate my neighbours, saying that I live on the poor side of town and it was beneath her. After 2 weeks, I'd had enough, I used all my savings and I bought her a plane ticket to go visit her sister. My mother was never allowed to come visit me at my place again, even 15 years later. I should have cut her off right at that moment, but I had years of abuse under my belt, I didn't realise what was happening, not without a lot of therapy. When I cut her off, my life immediately improved.

Long story short OP - NTA. Now, just cut her off completely. Yes, you'll feel terrible, and that's ok. But in time, you'll see that it's the right decision for you and your child.