Hmmm, im not sure about this, but I want to learn about hpw someone would handle this, so im just going to say what I THINK would be good, and then see what everyone elses says ;)
Are you doing groundwork with her? I think that could help, it might really help you guys figure out that you are dominent, but if you pick the correct way with a good teacher o teach you how, you don't have to use exessive force. Then maybe she wouldnt challenge you like that. (im guessing she's challenging you, I havent seen her do it, so I don't actualy have any good idea)
Without a whip I always use body langauge to get a horse farther out on the lunge, and if they ignore it I go "SSSSSSSSST!' but im not sure if that would work here, I've never actually lunged a horse like that.
It might just take time? Is she a lazy horse? If she's not lazy then maybe you could just lunge her at the walk, and ask her to trot with your voice, and maybe she will get bored (like I've seen a lot of horses to do) and start trotting, then you could praise her a HUGE amount and love her to death and show her how good that was! But when you see she's about to trot because she's bored, make a specific sound you will always use to make her trot, like a cluck or 'kiss' or something. :) and try that everytime she does that?
And for the whip, im not sure about this, just a guess, but maybe you could bring her into the arena or something with a halter on and hold a whip, and if you jsut holding it sends her into a fit, then hold it and feed her treats and stuff until she calms down a bit, and do that everyday until she's fine with you holding it, and then touch her with it slowly and just leave it on her ex.shoulder until she calms down or at least doesnt act so stressed, feed her treats and stuff. And just keep going each day without rushing it until one day you can ride with it! But that's jsut an idea, I've never seen anyone do this, or heard of anyone doing this,just something I think I might try :) but maybe try it once you have a good strong relationship with her, unless you already do :)
If there are no horses in heaven... im not going.