I kind of wonder if she means that MIL is holding the baby in bed or on the couch and ALSO napping (i.e., co-sleeping), and the LW is saying it unclearly.

(Don’t want to get into a co-sleeping debate, I did it with my own kid 26 years ago, but recommendations have changed since then, and I’m OK with LW calling the shots on what she’s comfortable with.)

I agree, though, that “not safe” and “won’t babysit when we need it” doesn’t quite gel, and I have a feeling there is a lot of history unspoken in this situation!