I'd get out while you can! Sounds like a very difficult client. And right from the start there is very little trust. This sounds like a family you will have to constantly be bringing out the contract with.

Questioning the $$ would be a huge problem for me. If they are paying more then they think they should be paying then no doubt they're going to expect the world! Early drop offs, late pick ups. They sound like the kind of people that want to get their moneys worth!