Mother in law

So ladies how many of you are in relationships with kids that isn't yours? Me and my boyfriend both each have one boy. And now expecting one of our own I'm 10weeks. He's son goes to school now but mine is young and is 3 only. So my boyfriends mother have offered to watch him will I work since we moved down south where she lives. But now my boyfriend tells me I can't work anymore because she doesn't want to take care of my son anymore because we fight as me and my boyfriend fight and she wants nothing to do with us. Is that okay? Because I feel like it's not fair at all, he tells me she was just helping me take care someone who isn't even her blood. But he tells me this last minute that I have to quit my job. I feel like if she wants nothing to do with my son and doesn't want to help me babysit him while I work so I can get my side of the bills paid because me & him fight ? I'm confused by that and gets me so mad and don't want her near our new baby. Am I right why to feel this way?