At opening, we have breakfast (if the kids brought it) and free play. We don't have any group activities like circle time until about 9 a.m. when most children will have arrived. IMO, it would be difficult for you to do an activity while new arrivals are being dropped off. Free play is not a bad thing at all. Children need to be able to entertain themselves and don't need everything to be scheduled. I don't understand why some parents think it is a bad thing if their children are not directed in what to do all the time.
Does this family realize you are opening early for them? If so, I don't know why they would think that your group activities would be started before you are officially open and before any of the other children arrive.
Maybe you should "remind" them that your official opening is at 7:45 so any activities are set up and done sometime after that time.