I think you should let her stay. You and DH are going to be so unbelievably tired after LO is born. There are things your mom can do for you while you are recovering.
When M and D were born, DH had a week off from work, then my MIL came over every day for a week, and then my mum came up from VA and stayed with us for a week. I was so thankful for all the help!! Granted, I'd had twins, but it was still such a blessing to have people there to help me!
This time around, DH is taking a week off from work AND we're having a post-partum doula stay with us the first week. And then when DH goes back to work, I'll have my MIL come over for a week and my mum come up for another week. Then my step-mother will be coming over in afternoons to help out with the twins and tired mama.
Everyone tells you it's the hardest thing you will ever do, having a newborn. But no one can ever really tell you how hard it is. I remember before M and D were born, I'd told everyone I didn't want anyone over for the first week so we could bond as a family. I'd pretty much changed my mind the first day there were here!!
Unless your mom is a mooch who won't lift a finger, take all the help you can get wherever you can get it!