^^Agree with how Cherie has explained. I would also be careful about fast trotting on tight circles & would be hesitant about doing any cantering on lunge or roundpen for the time being too, considering her age.
I felt like you didn't really answer my question and just said that I'm training my horse sloppily.
I don't have access to many jumps or trail obstacles at the barn I board at... I have some jumps but she is far from ready to jump so I'm not doing that.
I said that I use the lunge rope when I'm out of the round pen. I go into the riding ring and use a "corner" of it (it's oval so it doesn't exactly have corners) that help with her shaping part of the circle for when she canters. Walking and trotting, there is slack in the lunge line and she is incredibly responsive and gentle. If she comes in a little, I'm able to say "out" and she goes back out. She speeds up and slows down according to my commands. I guess using the word pull was a bit much when I ask for her to canter. I'll make the noise that she associates with cantering. If she's near that little bit of fence, she picks up the canter easily, but after a few strides when there is no fence, the lunge line goes from slack to really tight. I hold steady, but she puts her head in (from the tightness of the lunge line since it'll sometime be at the end) and drops to a fast trot but will pick it up again near that bit of fence... I just feel like she hasn't developed the balance or something needed to canter in a smaller circle.
It's only getting her to canter on the lunge line... Everything else she does is smooth and as it should be.
OK development aside, I'd get her lunging(on a line, not free) really well at walk & canter, on a really long line first(eg. Reliable on a slack rein), then ask for a canter when she's up to it on a really big circle. Fast circle work can be quite tough on their joints, especially immature ones, so the bigger the circle, the easier they find it.