Wow sorry you have to deal with such a thoughtless person.
I did an overnight for a family who welcomed their 2nd child over the summer also since they have no family close by to help them watch dcg. I offered with some hesitation at first but in the end I was ok with it because I knew they wouldn't take advantage. And it was still hard to do even though they were respectful of me.

You're going above and beyond what you would normally do so be sure to do it on your terms, not theirs. You offered overnight and they turned it down - don't understand why unless it's that they didn't want to pay for it? With so much family in town they should be able to make it work somehow