After some advice on how to tackle this situation with DM.
My husband is my nominated birth partner. However, recently when we were attending NCT classes he confessed to feeling very squeamish and uncomfortable when discussing labour and birth. At one point in the class he went very pale/greenish and had to put his head between his knees as he thought he was going to faint! This was just TALKING about labour. Bless him.
I decided to put my sister as a 'back up' person on my birth plan, just in case DH does pass out or have a funny turn during labour. My sister is very pragmatic, practical and level-headed and would be a good advocate on my behalf. Plus, she lives 10 mins from the hospital and is a teacher so will be off work around my due date (August) and available at any time. My DH will have her number JUST IN CASE he needs to call her but she absolutely understands that this is purely as a back up and she is anticipating not being called at all.
My DM doesn't live too far away, but it's across a body of water which she physically won't be able to cross if I go into labour in the small hours as no ferries will be running. I told her my intention to use my sister as a 'back up' birth partner and she was a bit affronted, but seemed to accept the logic (ie. my sister is nearer, more readily available to help, etc.)
I met up with my sister for a coffee on Saturday. She wanted to give me the 'heads up' that mum had told her in no uncertain terms that she was only to act as a back up birth partner if my mum wasn't available, and that- as soon as my mum arrives at the hospital- she is to take my sister's place at my side!
My sister challenged her by saying "but your name won't be on the birth plan, mine will"...to which my mum replied, "I'll just lie and say that I'm you!" 
There are several things which piss me off about this. Mainly her sense of entitlement, her assumption that I would want her there and lack of understanding that the 'back up' is purely that, in the unlikely event that DH flakes out. To be honest, I also just don't really want her there. Unlike my sensible, level-headed sister, my mum is very emotional (which will only be polarised by the circumstances) and a bit of a know-it-all. I can just see the midwife asking me a question and my mum butting in with the "Oh no, she doesn't want A...trust me, I've had four kids...B is better" bit and trying to take over, which will inevitably stress me out.
I do love my DM and I know she's just excited (first grandchild), but she seems to think that she's entitled to be at the birth when really the only people I want there are DH and the medical staff!
I asked her if her mother was present at any of our births and she scoffed and said 'of course not!'. SO WHY DOES SHE EXPECT TO BE AT MINE!?
How can I diffuse this situation without upsetting her? She does take any sort of rejection very personally, and gets very passive-aggressive with it. It's really the only thing that's stressing me out about the birth at the moment. 