To both Creampuff and Cascanastargazer; thank you for the detailed advise !
What I meant by not hurting her... I guess I phrased that wrong. I know I won't hurt her unless I really mean to. Which I would never. But I meant that I wouldn't like her to desensitize. I do hope that's the right word... I mean I've learned from a friend who's been riding all her life which is about 20 years, that when she keeps her head up too high or tosses her head to keep the reigns very tight and not lose like you usually do when western riding and hold one close to get her in circles, basically like Creampuff explained.
I think you are right with the guess that she's playing with me and it is a respect issue. As I'm still rather new to this, I find it hard to find the right way to show who's in charge. But I'll get around it with a teacher !
Thanks everyone for the replies, it really helps !!