Is she green broke and not understanding what you are asking for or is she acting up and just not wanting to listen to you? Most of our own driving horses would buck or spook too if I hit them with a whip while they were trotting.
She may think you are punishing her for doing something wrong or you may just be making her mad.
I only have one driving horse that I ever use a whip on while trotting and it is because he is lazy and will poke along if I let him.
(no, I don't actually beat him,
but I love the chance to use that icon when I get a chance) Unlike our other driving horses it doesn't faze him one bit to get a little pop with the whip once in a while but he is an exception. I could be wrong but I think most people don't use the whip to ask their horse for an extended trot. I personally just use a kiss noise to get ours to speed up and extend their trot and then I collect them more and tell them "easy" when I want to bring them back down to a pleasure trot.
If you are in the process of training the horse and she just isn't getting it, maybe you could try slowing the horse down to a very slow trot and then give her the kiss noise and let her out a bit when asking for speed and extension. Doing that might help her understand what you want.
I got a GREAT book about driving that you may want to look into buying. I think Heike Bean's "Carriage Driving: A Logical Approach through Dressage Training” is very, very helpful. I've read different sections in it many times. There are quite a few good chapters on starting the young driving horse including all the groundwork, teaching whoa, and the things the horse should be desensitized to before being hitched.