A.B.
I think they do have to take them outside... but they should DEFINITELY be doing it in the morning before it gets hot!
The shoe thing is a fire regulation... we weren't allowed to take kids shoes off at the daycare I worked at.
I just found a place to put my son in for the fall. I looked at several locations and a few did have indoor play areas for when it was raining (including the one I decided on). This one also has cameras. A lot of places out there have them... and some of them even have it where you can watch your child on a webcam.
I'd just look around. It took me a while to find a place that I really felt comfortable putting my son. Not that the places had anything wrong with them... they just didn't feel like the right place for us. Then I walked into this place and just knew it was the right one.
Always trust your motherly intuition!
Good Luck,
A.