First thing - as many have said, the ONLY person with any form of 'rights' here is the WOMAN GIVING BIRTH.
If she wants to tell the milkman but not her own mum that she's being induced, if she wants to have her mother there but not the baby's dad - sorry, but that's what goes. And the verrry simple reason for that is that birth is NOT just a medical process. It is a deeply EMOTIONAL process - as we all know, a woman whose feelings and wishes are respected in labour is likely to have a better, easier birth. Quite literally, you have a situation where the OP's right to maximise the chances of her being relaxed, and confident, and less likely to need intervention - literally, less likely to end up with damage or a CS - well, there is simply no comparison with any perceived 'right' of the MIL to not feel excluded in some way. Or OP's mum, if that was the person she wanted to exclude.
That brings me to the second point. Cricketballs and the other 'mums of boys' up in arms at this situation - have you read the OP's comments? She isn't 'excluding' her MIL because she is her MIL and thus somehow less central, less worthy, less family, she's excluding her because she's the kind of person who will turn the whole thing a complete nightmare! It's nowt to do with whose mum she is! The situation could easily have been the reverse - I'm sure if MIL was level headed, calm, sensible - as she's twenty minutes down the road, she would indeed have been the one the OP and her DH would be calling on, and if her mum was the one who happens to be a complete bloody drama queen, she'd be the one getting excluded. And quite damn right too!
Don't jump in going on about your 'rights' - you have none, as this shows. Instead, reflect on the universal truth and the moral of this story - that no matter what your relationship to a person, if you want them to want you around, if you want them to let you into the more personal parts of their lives, don't be a habitual pain in the ass. Because no one has a genetics-given right to nosey their way into any part of another person's private life. And in many ways, birth is about as private as you can get.
So, mums of boys - less about the rights, let's hear more about all the brillant, supportive, sensible MILs who have fab relationships with their DILs because they are nice normal people who don't tantrum, control, overreact, push their way in, and who are liked and respected as a result.