I have an older tb (19 years old) gelding who has always had rough canter to trot transitions but lately the problem has been more of a problem. The horse is a ‘been there done that’ type and knows his stuff, lately he warms up perfectly soft and relaxed for walk/trot, but when canter is added he is stiff and difficult to collect and even more difficult to get him to transition down to a trot. He will even throw in head tosses indicating his unhappiness. Once he does trot it’s a horrible down hill way too big trot that almost feels like his back legs are taking huge steps. Very different from his normal trot. He will jump a small course and do clean leads but gets stronger and stronger until he starts tail swishing and the head tossing when asked to tone it down. He does the same transitions when loose in the arena. I do have a vet coming to do a physical but I’m just looking to see if anyone has any insight. He looks sound and when loose in the arena has a ton of energy and has big elastic gaits.
Uncomfortable downward transitions from canter to trot can be a sign of hock issues and hock injections might be all that is needed to make him more comfortable.
I think horses have a world-wide contest going on. When they are getting all the aids & cues for the transition, actually they are competing against each other on how many times can they wobble around the arena without actually transitioning, up or down. Of course there are some well-trained horses out there who pick it up instantly. It’s just that none of them are on the lesson string. 
I was going to vote hock or stifle. Likely hock since he’s 19, if this is a new thing and nothing about his routine and fitness has changed. That would be my first thought!
I would agree with the hock theory. My mare is super hard to transition from canter to trot when her hocks are due, in addition to her other “tells”.
A been there done that horse suddenly resisting a basic command is very likely to be physical. I also vote hock or stifle as most likely.
Another vote for hocks being sore
This is a pain reaction. At the very least discomfort. Could be SI although that’s less likely than hocks or Stifles. Horse is telling you that he finds it hard to carry himself on his hind quarters for an uphill, light, down transition to trot. It would also be a good time for you to review how soft and “through his back” he is in general. Lessons with a Good dressage practitioner would be helpful
