S.M.
Well, I think that you should be there for your neice if that's what she wants. BUT... SHE needs to communicate her wishes in no uncertain terms with her mother and the hospital. She is an adult (or about to become one very quickly) and it is not your job to tell her mother or work it out for her.
In terms of her mother, if she attacks you on this topic, I wouldn't take sides. Just say that if there is a problem between her and her daughter, you aren't getting involved. But you will be a support in the delivery room since she asked. And you hope they work it out.
I would also suggest you urge your neice to find some role for her mom. Say, "Mom, you and I get on each other's nerves, so I think I want Aunt K. to be my main coach. But Mom, I want to make sure you are first to hold the baby. Or I want you to come to the hospital and into the room when I start pushing. Or can you pick out the going home outfit." Or what ever works. The truth is labor is flexible and long and has stages. And having someone else there even intermittently is not a bad idea.
This is HER birth and she should totally be in charge of her labor and delivery experience. However, as she becomes a mother, she needs to recognize that her mother loves her, and she should want to encourage a loving grandmother. Yes, set boundaries, but be mature enough to include her mom in a productive way. I know there are some awful relationships in the world, some that are simply too unhealthy to continue. But if she is in contact with her mom at all, surely she can assign her a meaningful role to include her in the birth of her grandchild (and keep some peace).