If they've agreed already to hold the fort with your dd's, then yes totally unreasonable. I'd be really upset and would feel vulnerable. But to make yourself feel back in control again, all I'd say is think very hard now about an alternative back up, and run with them instead. Not easy I know, but so close to the birth you don't want to be feeling so let down by people you though you could trust.
Talking of which...
My first labour was a fastish 4 or 5 hours. 21m later, with dc2 imminent, I'd been warned to expect quicker next time. Mil happily agreed to be on standby to look after ds1, on whom she doted, while dh and I went to the hospital with my independent mw. She appeared totally happy and enthusiastic to be involved; I kept checking she was sure she'd be OK if we called in the middle of the night etc. Yes yes yes she said. We'd talked it all through; she's max 20-30 mins away, albeit she doesn't drive. But she was to jump straight in a cab, or get a lift if one was available (sil was around the corner and willing to do this if around). There was even a direct bus route to drop her off at the end of the road if the traffic was OK. So we all thought 40-45mins would be plenty of time to allow us to get away together.
So...mil gets the call 7am ish. Good I thought, just before the rush hour but not in the middle of the night either.
But the cow took over 2 hours to get to our house; dh was beside himself as he wanted to be with me at the birth. He missed it as labour was 2 hours. I was really pissed off.
She'd decided to have a shower and wash her 3ft long hair before calling a cab.
This was after we'd carefully explained to her that she was needed BECAUSE my first labour had been so quick.