The handicapped entrace does bypass the stretch room, but it requires a CM to lead you thru to the entrance door. So, it's not something they can do very often or when it is busy. So, if you do ask, wait until the line is very short.
I guess, for a child, I would try to find out just what it is about the stretching room that scares them and try to come up with ways to handle those things instead of trying to bypass them.