Generally a horse who is rough in the trot or canter will benefit from comllection work. You did not say if you ride western or english, but what I would try is to work on his collection. Start at the walk to help bbuild up the right muscles and if he is not well colledted int he first place, then only for a few short minutes at a time and gradually build up to longer as his muscles are not used to that position.
One other reason that he could be rough is his conformation. If his pasterns are really short and fairly upright, that could be one cause of his rough trotting. However there is also a possibility that a different hoof trim or shoeing angle would help.
There are to many different possibilities at this point with out knowing all the details of the horse and his conformation.
You might want to consult a vet and a farrier or a conformation specialist like Dr. Deb Bennet and get an assessment of his conformation to see if that is the biggest problem or if his problem is a lack of collection.
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