First it does say a lot about you and your program that the family wanted to keep the children with you. However, this is one of those cases where it would be better for everyone - parents, kids, caregiver and caregiver family that they move on to new care arrangements in the new town.

You might even put it that way to the family saying you are grateful that they liked your program enough to want to leave the kids with you but that you feel it isn't fair to the children or your own children because of the change in pickup time. It is a long day and everyone just wants their own parent by then. So you will keep them for a few more weeks - say end of June is enough in the sense that they can get a high school student for the summer in their home so they are not without options and have till Sept to find someone new.