If it were me I would return their deposit and keep looking. My hours are my hours and I do not work past that even if it is only 15 minutes on occasion! As for the schedules being all over the place, that wouldn't bother me as much unless you go on outings and walks and you will be sitting at home waiting. I just carry on with my day and our routine and if they kids aren't there yet then so be it. Once everyone sits at the table to eat I do not make food for a child who just walks in the door. Same with arts/crafts, if they aren't here to begin with the rest of the kids they certainly don't get to take part if they come in the middle of it.

If I were you I would tell them your hours are 7:15 - 5:45 and not a moment earlier or later. If that doesn't work for them then so be it.