I could not find any signs on my way in but I did double check on the way out and found this. It was VERY difficult to see and two large panes of glass away from the actual door itself, the spanish version was over to the far left on the other side of the doors as well.
Owned by the city or not this sign is practically invisible.

Just thought I would share in case anyone else googles or searches the forums for info on the Houston Children's Museum. I still don't know if they are owned by the city but I would guess "probably so" because they had a HPD Office "guarding" the front entrance at a booth there.