Why does it shift better on the trainer?
 

The RD shifts much better on the trainer than it does on the street after I adjusted it while on the trainer. On the trainer it shifts fast and smoothly now. On the street it will shift just like on the trainer at times, and hesitate at other times. The rear skewer is on tight, will using more force to tighten it make it shift better? Adjust it again but without the bike being in the trainer?

Chances are you are nice and comfortable on the trainer and can shift easily. Out on the open road, you and your bike are dealing with a lot of other forces/conditions that you don't get into indoors.

Take the bike for an easy spin on a flat, smooth back road or empty parking lot and shift through the gears while concentrating on shifting smoothly. If it works in that case, just pay more attention to your shifting.

There is les load on the drivetrain on the trainer. Same thing happens when working on one in the repair stand, then test riding(which is why you always test ride a repair)

If the rear derailleur hesitates when shifting to a larger cog try a 1/4 counter-clockwise turn on the barrel adjuster. If it hesitates when shifting to a smaller cog try a 1/4 clockwise turn on the barrel adjuster. If the shift cables are old or corroded replace the cables and housings.

Al

Frame flex.

Thanks for all the replies, I've still got more work to do here.

Bingo.