Idk how to tell my bf I don’t want his mom watching our toddler anymore or IF I should tell him the reason why

Need opinions. I found out my bfs mom was talking bad about my bf and I as parents. We have a 2 year old and im pregnant with our second. I have lots of doctors appointments and don’t have much family on my side that help with my toddler or baby sit, so my bf always wants his mom to watch him when we go to appointments and stuff. I’ve never had a problem with her baby sitting because she seems to love spending time with our child and a lot of time will ask for him to come visit or ask for him to stay the night etc. the ONLY time we ever ask her to watch him is when I have a doctors appointment because children aren’t aloud at the place I go. Any other time she has him is because she asks us. Well my sister told me a few nights ago that my bfs mom was saying all kinds of things about us as parents to my other sister and told her to not repeat it or tell me. Well of course one of my sisters told me behind the others back, she said that my bfs mom told her we are “dropping the ball” as parents. Said she’s our child’s grandma, not his babysitter. Claimed she “has our child more than we do”, claimed we never feed him and he doesn’t have any clothes so she was gonna go buy him clothes. And even said someone needs to “step in” because she would hate to call DCS on us. I was so confused and hurt that I literally just cried when my sister told me this because I didn’t know what to say or know why in the world she would even think or say those things. Any time I’m around her she always talks about how good of a mom I am and how she loves me and my child and she’s always here if we need help etc etc etc but then gonna go say those things ?? All of which are absolutely not true in the slightest. So now I’m not comfortable with her baby sitting anymore knowing that’s how she feels, I have an ultrasound appointment next week and my bf of course wants his mom to baby sit and idk how to tell him I would rather someone else watch him. I want to tell him the things his mom said to my sister but he’s either not going to believe me (because I myself didn’t even want to believe his mom would say those things) or he’s going to be absolutely furious at his mom and it’s gonna be a huge ordeal and then he will be hurt after he’s not mad anymore knowing his own mom think that of us. When my bf gets mad he has to cause a scene and I want to avoid that and just avoid any drama period. I hate conflict, it’s a childhood trigger for me. I don’t even care about addressing it to his mom because I know none of the things she said is true so I honestly don’t care how she feels about us. But I know he will want to call her out and make a huge deal out of it which I couldn’t blame him for doing, but like I said I just want to avoid conflict. I would rather not even address it or put any energy into it and just not allow her to baby sit anymore but idk what to tell my bf. What should I do?