OP, trust your instincts! From what you've said, your MIL is one of those mothers who are domineering, and who think their adult children are still children. They think that they know best.
Do not use her for childcare, or she will ignore any instructions, such as nap time, or not allowing certain foods etc, because she did it in her time, and DH was absolutely fine, and unless she tells you she's done/not done, something, you won't know.
People telling you she's doing it out of love, don't consider that not everyone is as lovely as their DM/MIL.
You know her better than anyone here, so if you're feeling uncomfortable about certain behaviours she exhibits, then trust your feelings, and set boundaries.
There are people on here who will tell you to ignore the "MIL haters". There are no "MIL haters", just people who realise that not every MIL is the caring, loving kind, and will call that out. It's not a blanket hatred, and it's ridiculous to think it is.
Your DH has the measure of her, which is really good. A lot of the son's of these types of MIL don't have their wives' backs. You can work as a team in setting boundaries.
I say all this, as a grandmother myself. I wouldn't dream of doing the things you've described your MIL doing, but it doesn't mean I don't love my GD. I just know that she's just that, my GD, NOT my child, with a baby maker being the one who grew her for my benefit.
Good luck with setting the boundaries. Don't think of it as "confrontation", think of it as being assertive, so you can bring your child up in the way you want them brought up. You and DH are the parents, so what you say, goes.