Charging Hourly vs. Flat Rate?

[Angelsj]

Anyone else bill hourly? Or does everyone just do the flat-rate with contracted hours, and bill extra for overages?

I bill hourly. I am not going to lie, it is not the easiest way to go about things, but it is what I do. I also take a LOT of part time/drop in kiddos. It takes some work to balance time vs money, and part time vs full time.
It can and is being done, but the concerns the others have are valid. You must decide if you are willing to put forth the effort.
If your issue is parents not following the rules, hourly is not going to fix that for you.