Haven't read all the pages but I do think absolutely YANBU to not want to be swarmed by your MIL at a very private and vulnerable time.
OTOH, it is possibly U to mistake this for your MIL not caring about your rights and wishes. A lot of people make the mistake that this specific time (labour and birth) is about the baby, and not YOU then the baby, if that makes sense?
She is thinking about her son's child being born, the two grannies being there, her excitement, wanting to be there for you both, etc.
I remember my MIL with my SIL when my nephew was born saying (as we were all trying to slot in to visiting hours) 'Can we go back in again at visiting time 2?' and him saying 'I don't really know, it depends how DP is feeling and what she wants.' My MIL then said 'Just remember, he is your baby too'.
At the time, if anyone had heard her they would have done the RL version of flaming her!!!
BUT I knew that she was worried about her son feeling useless after a bit of a traumatic birth, trying to keep him involved, trying her best to be involved as a grandparent and GENUINELY thought she was helping. Of course, she had overlooked the fact that my SIL is v private, pleases people all the time and wouldn't ever say she wasn't up to something.
My BIL, however, has no such issues and said 'yes, but she's the one who just had f**ing stitches in her vagina and no sleep' 
She got the point! And in case you missed mine
DEFO do what you want, but don't get stressed, she probably doesn't mean to make you feel that way.
Tell DH to say 'ooo we can't WAIT to see you and ds together! We are soooo excited, he will love his granny! We will be phoning you the very MINUTE catholic is ready so you have the nicest visit!' etc
Good luck! x