There are many questions that you need to ask a trainer before you allow that trainer to work on your horse.  I 've seen a horse that had a good disposition turn into a skittish horse just because that so called trainer used spurs on the horses neck.  That trainer was spurring the horse so much that the horse couldn't think of anything but the pain it received when someone rode it.  Horses aren't naturally mean.  A trainer that doesn't know what he or she is doing can make it mean.

Ask if you can visit while the horse is in training.

If the trainer is going to train the horse right he won't mind if you are around watching him.  Most trainers want you there so they can teach you at the same time.

Ask for references

The trainer should be glad to give you references.  You would check out a doctors references if he was going to operate on you.  Why not do that for your horse.  I'm sure the horse would appreciate it.