In addition to what I suggested previously, I also think you should develop some techniques that will help your horse respect the bit rather than using a kimberwick and then expecting the same response when you change to a snaffle as it won't happen like that!
Why don't you try working the horse in the kimberwick for the majority of the ride, then when she is responsive, switch bridles back to the snaffle bit. Work on getting respect from her whichever bit you happen to be using. Gradually, try riding every other ride with the snaffle only (e.g. if you ride four times a week, alternate so you ride kimberwick, snaffle, kimberwick, snaffle). Make sure that when you ask for a half halt or a downwards transition you GET the desired response - ask, ask, TELL. What I mean by that is that you ask for the response, ask again, then you TELL her. One good excercise I have found to work on horses that ignore your commands is to stop and back four paces, then continue. This is a lot of work and you may find that your workouts extend far and beyond an hour or two depending on the horse. The point is that you want an instant reaction when you ask for it, so make sure that you get it. Your horse will soon find that it is much easier to work nicely and calmly than it is to constantly stop and back up every few strides.
People on here (myself included) get a little tetchy when the subject of bits is brought up and with good reason - many bits are used for purposes other than what they were designed for. It is fine that your trainer suggested using a kimberwick as a training tool, but did she have a strategy for its impementation? What were you going to do differently with this bit that you weren't doing with a snaffle previously? I.e. Were you given advice on how to use it with the ultimate goal of schooling back to a snaffle? The reason I ask is that if you continue to use the kimberwick as if it were simply a snaffle with better 'brakes' your horse will develop a harder mouth over time and you will find yourself in a real pickle.
Another thing people get hot over (again I am guilty of this) is 'trainers' giving less than creditable advice, particularly when it comes to the improper use of tack and gimmicks. There was a thread on here somewhere a while ago where someone happened to mention that their 'trainer' had advised her to sedate her horse before a lesson, can you imagine? People who use running martingales to keep a horses head down is another pet hat of mine. Sorry to use you as an example Beling, but tightening the flash on a noseband is precisely what I am talking about. All these measure might be a quick fix, but is not in the long term interests of the horse OR the rider.
As I said, using the kimberwick is OK as a training tool, but ask your trainer how she plans to help you wean yourself and your horse off that bit and come back to a snaffle, it could take considerable work and patience on your behalf but you will be a better and more knowledgeable rider for it. Honestly, I hope you guys have success and I am sorry that you feel you have to go back to 'lurking' on this forum, it's just that some of what you said hit a raw nerve with some of us that have heard similar stories many times over. We probably should bear in mind that this may be your first experience in this situation, doesn't mean you don't know anything about horses or dressage, just means that you need some help with a problem you may not have encountered yet.
All horses deserve, at least once in their lives, to be loved by a little girl.