I ended up taking them for this week. I finally got an e-mail from mom at 11am after I gave her a deadline of noon. The other family is totally fine with starting next week, so I told her this is their last week, PERIOD. I know she's upset that she has to find something to do with them next week on Veteran's day, but oh well, not my problem! If she didn't want to end care, she shouldn't have given me notice! The kids got off the bus here yesterday and dad picked them up. I went ahead and sent home all their nap stuff since they won't be napping here anymore and reminded dad AGAIN that this Friday is their last day. Mom paid me in full for the week yesterday when she sent the e-mail, so after Friday, we're good!
I still think it's ridiculous that they are choosing to pay me for another week when mom is working from home and Dad gets home about half an hour before the bus drops off right in front of their house, but I guess I'm just weird that way. ;)