Ask your daughter what she wants! If your son-in-law is not controlling her in some way, she can sort it all out. It sounds as if he's getting a bit nervous about the birth, and is striving to 'be in control' of himself. Probably feels that he has to be the strong one in this situation, and take care of his wife.
Whichever way it goes, you must make sure that your daughter is happy with the arrangements.
And do ask him to ring you when she goes into labour. That's the very least he could do!
And if I were you, (speaking from experience) I would pack a small bag: bottle of water, flannel & soap, hairbrush, and a packet of daughter's favourite biscuits - just in case they change their minds at the last minute!
Good luck, and congratulations, Grandma!