oh no, that's tough call!
i have part time clients too, and they pay in advance beginning of week-- Monday. and they give me schedule in advance. they call when they need more days.
They know i have daily outings, so if they come in late, i won't wait for them. there is a note in the door - say, library, park, playgroup. good luck finding us!
we need to plan our days, so parents should consider this when asking for part time spots.