Stretches are meant to have an effect, it is unlikely to not feel anything.
You surely find information about that somewhere on the internet, perhaps with more details to what you should feel with a particular stretch and what you shouldn't.
Normally gym leaders are quite flexible and can stretch more than anyone else. It must not be a problem if you can't go as far as she can, neither for you nor for her.
Should I complain
No, first of all just talk, don't yet complain
to the store manager
No, talk to the leader first. Why go the way top down? This is a bad image upon you.
How can I refuse without making a scene?
If she calls you out first of all tell her it hurts and ask if it should. Ask what you can do to do the excercise without having a problem.
After class you can tell her it's uncomfortable to be called out like that, ask her to do that another way.
I believe other people feel the same way as I do.
If you want to use that for an argument, don't "believe" but be sure they really do.