Agreed with the trainer. There are a million differant pieces of advice I could give you for every certain situation, and it would be impossible to get it all down on paper.
Before you go off to the trainer though, I would reinforce all buttons (Haunches/forehand/sidepass), led yields, and just make sure theres a good foundation so the trainer only has to start patterning and getting him "Rodeo Ready" as my trainer calls it. I know that at my barn, I get VERY frustrated when people send their "Barrel horses" out and expect a miracle when they have no foundation for it and we have to go through ALLLL he basics again.
Things like moving body parts, a soft and supple mouth, flexibility, respect on the ground and in the saddle, decent transitions already and knowing their leads. Backing up, able to back up squares/circles, counter flexion is nice to have but not excessively necessary, it's easy to add on to a horse with all the other buttons.
Storytime. I once had a girl bring me an unstarted colt, saying she had a rodeo in a MONTH that he had to be ready for and she wasn't paying us unless they were ready for it in that month. Yeah. This is an extreme case and obvious your horse isn't an unstarted colt, but needless to say a horse without foundation sent to a trainer for a specific thing is irritating unless they are actually sent there to get a foundation in the first place.
I'm rambling/ranting, but that's my little slice of advice.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.