I completely understand where you're coming from. You need to focus on your delivery and the new baby, and don't need this added stress. Personally, I think that people should cater to the new mom around the time she gives birth because of everything we go through in childbirth. It's a given that most of us are going to want our mom around right after we deliver, not necessarily our MIL.
But as someone else said, your husband feels like you're saying his mom isn't good enough and is probably offended by that. I think your issue with your MIL is bigger than just having her watch your daughter for a couple of days when you're in the hospital, and understandably so. I wouldn't want my baby eating crappy food, etc. either. But I think too that as moms, we worry a lot, and usually the things we worry about don't come to fruition.
Your MIL loves your daughter and wants to help so unless she lacks common sense, for example if she's the type of person who'd leave a baby alone in a bathtub even for a second, or if she leaves things around that could be dangerous for your daughter, it might be good to let your daughter stay there just to keep the peace in the family. Your daughter will be fine in your MIL's care, and if anything happens, you will have a stronger case for not leaving your kids overnight at her house in the future.
Hmm... one thing you could do is let your MIL babysit a lot leading up to your due date, and if she complains about your daughter at all, then you can offer to have your parents take her instead. I believe your MIL wants to help and feel needed, so if there is anything she can do to help you, unless she's going to gripe about it, you should let her.
Congratulations on your upcoming new arrival and good luck! Don't stress and keep your mind on the new baby.