It seems so wrong that you feel unable to have your mum there, even though you want to, just because MIL is feeling put out etc. Your first experience of birth should be as you want it to be!!
I do wonder if asking her directly why she feels she will be the last, be left out etc might be worth considering! What has made her feel that way? I am not suggesting that you have done anything to cause it.. more that calling her out on what sounds pretty ridiculous, needy and probably born of some unexplained fear, might just open up a channel of honest communication. However, she doesn't seem like someone able to deal in a grown up way with issues!
I'm sorry you are facing this at such a special , exciting and a bit scary time
What were the first ever records that you bought and when?
To think that London, or anywhere else for that matter, does not belong to any one demographic