at this point i would ask one more time if he is prepared to promise to be there in good time for you to pack and go away... and if he ums and ahhs, or is in any way not certain, i would immediately do as you say and book the night nanny on his cc. and not even bring the subject up again.
if he then questions why you did that, you can calmly explain why. you have been utterly reasonable and bent over backwards to accommodate him and he has been the total opposite on the one occasion you have asked. your work required it, so you made arrangements to fulfill your commitments. simple as.
he is being a git.