Catholic - YADNBU. Having my mother there in labour is what I would want - she carried me for 9 months, she had me pulled from her vagina, she breastfed me 18 months, changed me nappies, blew my nose, did all the icky stuff for me when I was growing up. She can handle seeing my bits. She can help me latch the baby on when it's born etc. As lovely as my own MIL is, I'd prefer it if she didn't see my bits being stitched up! My Mum didn't have anyone when she had me, her mother was in a different country and she and my father don't believe men should witness childbirth. To not have anyone aside from a Dr was my Mum's choice (she didn't want her Mum there anyway, they're not close).
YOU are carrying the baby, YOU are pushing it out of your fanjo. YOU decide who is there and when. There is no point anyone arriving until the baby is born, no-one knows how long it will take, if you will need a CS or anything like that. Your MIL sounds overbearing - explain that she may see the baby once it's born and you're out of the delivery suite, cleaned up, stitched up and your baby has had it's first feed and been washed etc. Don't set a precedent for her to walk all over you, she's still baby's GM, she's still important and special but she needs to respect your privacy and see the baby once you're ready to receive visitors.
Your mother being present doesn't give her the right to be there - she is not your mother. I can understand to an extent why she wants to be there straight after the birth to see the baby but it's not a given right. My SIL gave birth 8 years ago, her mother and my DB were there. 24 hours later my parents and I went to see my DN but only because I was about to go abroad for several weeks - if not we'd have left it longer to give them space but they were happy to have us. We went for a few hours, had some cuddles, cooked her and DB dinner, made SIL drinks etc so she could rest and took supplies of food etc to save them a job.
If DP doesn't start sticking up for you tell him if he won't support you he won't be there either to witness it. You need to be as calm as possible during labour!