IMO I think 9 is a decent time for a 2yr old to go to be. I think it is fine.
However, I think children need to be on a basic schedule. My girls had a set bed time and they went to bed when I told them it was bed time. Every since they had a bed to go to. Of coarse it varied when they became of school age. Because of wk ends and summer time. But they always had a set bed time always. Until they became 15 and then I let them stay up if no school. They would usually fall asleep early because they were not used to staying up. lol