Tell your MIL not to worry, this delivery is more about the "help they are going to give you"... and not because they are the only people that are most important to baby... therefore she should not look at it as if they are only there to witness the birth, but to give you support thru this process in which you need all whom are your most needed support.
YOu can tell her, "listen, I love you and you are very important to baby.. "baby will love you the minute you hold him/her because it will be the love you give baby that will count from that moment on... not weather you are there on delivery or not... the delivery is really my time to peacefully bring baby to this world, but it doesn't mean I want everyone in the family there... I hope you understand that this has nothing to do with who is most important to baby, but it is more about who is most essential to providing me with what I need during that time of delivery.. and my mother and sister, and your son, are the support that *I need* to have that day... not to mention you are a great mother in law, but I do hope you undertand this is more about how I feel about who I need there for me as they are my coaches" etc. You can tell her in your own words offcourse, but basically you need to let her understand that your mom and sis, know exactly what to do to help you,and that you "need" them.. and it has nothing to do that they just want to see the baby first.. but that they are there to help you ease the pain. I mean that should sum it up. But tell her, that she can be the first to see baby right after.. that might ease her feeling of wanting to hold baby right away for bondness. But really, it is what happens during the time after that counts to her closeness to baby, not that she was present during birth. I think the only one that really matter in the bondness of baby is mother and father.. just because they are the creators of life, and therefore seeing baby born is their awakening as to the pain and love it all involves.. you offcourse love baby as mother, and father in turn loves you for all the hard work you did to have the baby.. But it's all how it feels after too.. father can be present at birth and have no involvement whatsoever.. so it really is about their involvement with baby once they are born...
Birth is your time with baby.. You can share that with your hudband because he is the creator of life.. and then after that.. whoever is there should be for support, and support only.. not just because they want to see baby be born. That is something very intimate and only you should be the one to choose who you want to be by your side..
I know I was not one to be so kind while giving birth.. so having people around me, would have put my nerves up the wall... so you really need people that would help you calm down, and ease you thru that time. Make this your choice... not hers. This is your time.
Good luck with making her understand that. And even if she doesn't, well, it's tough luck for her.. because you should not have someone there just because they want to see baby be born.. then you might have the whole family there making you nervous in this very personal time for you and baby.
Best wishes on a very calm delivery!