To me it sounds just like what my trail horse used to be like...he needed motivation and I wasn't finding what motivated him.
I will be the one to disagree with everyone, that force is not needed, it's motivation that your horse needs.
What motivates your horse? Treats? Play point to point...set up different things in the arena, whether they be tires, barrels or whatever and place treats to them. First ask her to walk to a couple. When she gets there, she gets a treat...motivation for her to go...then try a trot. If you don't have barrels or whatever, a friend is great to use. Have your friend go to random parts in the arena and just stand there, ask your horse to trot to her..if she trots with little to no effort on your part, and at least goes half way, reward for that, then start being more demanding. "Ok I know you can trot and you get the game, how about now we trot all the way with little to no effort".
Hitting the horse on the rump with reins or a whip or spurring them in the sides will work, but it's called a quick fix. You want your horse to want to trot when you want them to...not to be forced to when you want to :)
My trail horse now, the second I raise my energy, he matches that energy, whether it be the energy for a trot, or canter. We played point to point for a couple months at each gate until he was just able to match energy