I can see where everlong is coming from, but I really don't think giving birth should be seen as an opportunity for anyone else to have an "amazing experience". Birth is not a spectator activity. It's an extremely important rite of passage, for the parents.
Having the feeling of being "watched" during labour can raise Adrenalin which inhibits the flow of Oxytocin - the labour hormone that makes contractions happen. This is the very natural and normal reason why so many women want to create privacy during birth. I always cringe when I see mums on One Born Every Minute with an enormous entourage of bystanders (with partner, Mum, AND MIL "supporting", by the time both the midwives attend for the actual birth that's 5 watchers!!!). It is the perfect way to slow labour down and for complications to occur. THIS is the reason why most hospitals limit birth partners to 2 maximum (space is an issue too, yes).
Of course, some women like to have their mum or MIL there, and that would increase their sense of safety and security (which increases the flow of Oxytocin) and in those situations, it makes perfect sense for mum/MIL to be there. I don't think this is the case for the OP however.
OP - Get your DP to ask MIL what she intends to do after she has dropped you both off at hospital. If she had thought she would be there at the birth, he can gently explain that you want to keep things private. If he's kind about it, I'm sure she'll understand. I bet she just wants the best for you. You can't control people's reactions, but if you're honest and gentle about it then you have taken responsibility for your side of things.