This is my opinion but personally I would charge a daily flat rate as well, and i would need a better idea of the hours the kids would be there. If the dad got a full time night job, then is he working the same hours every night? If so, then he would sleep for a set amount of hours during the day, right? I understand that you are still trying to work out the kinks, but i always prefer more details. Are the kids coming every day now?

If you you feel bad about charging for a full day if they are only coming for part of the day, then charge 5 -10 dollars less, depending on your rate. if you regularly charge 30 per day, charge 25. You have to give them snacks and a meal, that means they are there for a good portion of the day. Don't undersell yourself. You are still working a full day regardless of how many hours these kids stay.