Unless he is consistent with his hours whether he uses you for 4hrs or 6hrs your whole day is shot. If you don't know ahead of time when he is coming and going you can't make plans or run errands or do anything but sit around waiting. Therefore, full day fees and he can arrive and go as he pleases (within reason) or firm hours with a slight discount.

All that said, I wouldn't take on such a family as it is hard on the kids to not have consistency and when it's hard on the kids it is hard on you.