I'm not a trainer by any means. However, to me it sounds like your trainer is trying to help you work on your balance. Forget about reins, and just balance while at the same time using your hands, and moving around in the saddle (putting the hoop on the fence.) She knows you can go faster, but she wants you to master your balance before you do this. Even if you feel balanced, there may be something she sees that leads her to believe you need a bit more practice. Especially if you hope to jump. Balance is everything! Trotting is the most difficult to balance at. Once you master it at the trot, cantering is easy. As well as the old saying, crawl, then walk, then run...
It would be nice, if she would share her thoughts, but then again... Maybe it doesn't really matter. If you can, do some riding bareback. Walking and trotting esp. It will help with balance. If you can, drop the reins and steer your horse with your body... If you want to go left, look to the left exactly where you want your horse to go, don't touch the reins, same for a right turn. (Some horses don't do this, so if yours doesn't, then um, nevermind.)
I would keep trying. Actually, I would try harder. There is something that your trainer want's you to understand/do/be able to do. And apparently wants you to figure it out on your own... I'm not sure the method is fantastic, but you can still do it. Try practicing more and harder, really focus on this stuff and be as good at it as you can.
Be the best you can be a putting that darn hoop on the fence! Then, I bet you will progress to something else.
Stick with it, hang in there. All good / great riders spend countless boring hours doing the same boring thing, until they can do it in their sleep perfectly. Then, they get to move on to something else.