I used to have one like this too and it drove me crazy!! I would text at 9 to ask what time they were coming and I wouldn't hear back for hours. They overslept, the alarm didn't go off, her phone was on silent, her daughter was up late so she let her sleep in etc etc. For the same reasons as you, it bugged me.

I repeatedly asked her to be there by 930/10 at the latest so that her child could get the most out of daycare!! They paid a lot of money for her to come here and basically just eat lunch and lay in her playpen (she wouldn't nap either on the really late drop off days) I explained that we did most of our structured learning in the morning and her child was missing out on this. They didn't seem to care. Mom worked part time and went to school part time (but on her own schedule) and had said on many occasions that she wasn't a morning person. I think this was the reason for the late drop offs.

I am not a drop in centre and I like to know when people are coming and going. I don't mind the odd drop off/pick up at a different time but a time span of up to 2-3 hours is just disrespectful IMO.

I think you are within your rights to ask a parent to be here by xxx time. It is your program and you have to run it so that all the children benefit the most from it. Waiting around the house for a child is not fun and really limits what you can do when you have to stick close to home/backyard.