I think it's a bit odd that your mum had an expectation that she would be there? Don't take this the wrong way, but surely she should be taking your lead on things and supporting your decisions?

Me and my husband made the baby, we will parent the baby and we will bring the baby into the world. I also want to make sure after baby is born that we get some time just the three of us before the grandmothers swoop! In fact, we've made it clear that they aren't to come to the hospital until we say we are ready.

I think you just need to stick to your guns and make it clear that you expect your mum to support your decisions, whatever they might be.