Have you visited the Montessori ? ds went to one which was disciplined but still fun and sociable. I think they vary as much as any preschools/playgroups. I visited a couple just to see what setup I preferred.
If the play group are relaxed about the times and you are happy with it then your instinct could be fine. Perhaps although they "open" at 9 the reality is that kids arrive in the next half hour or so as their parents also have other kids to drop off for school. Do they bring the kids together after a period of free play for a circle time or group activity a little later ? Can you visit again with dd to see what her reaction would be.