not by business, but I can't help but wonder why she wants to co-teach a fusible applique class when she doesn't think it's applique???
That being said, I co-teach a beginners class and our applique class includes needle turn, turned & machine sewn, & fusible raw edge----we teach that the basic process is the same with some differences in the prep and finish. Good luck--this sounds like it could be an unpleasant experience if there is already such difference of opinion!