I.N.
Daycare needs to be reliable for you to be able to work. Put him in a center. Home daycares can sometimes close at a moment's notice, if there's an illness there, etc., so a center would offer you more reliability. Explain it to her like that. If she gets mad, then she gets mad. You have to be able to work. I had this same problem when my MIL was watching my kids. We got along much better after I took the kids somewhere else.
Another possibility is to find a place you can use for drop-in care and use that when your MIL is otherwise busy.
Good luck!