You had moments where you can see what kind of team you guys will be (when you get there, I don't want to show against you).
Till then, you as the more advance part of the team MUST ride every fence. You know what they say about making assumptions... haha. I personally have nothing against trotting corners. But it should be done in an organized manner. Half Halt, downward transition, at least 3 strides of a balanced trot, upward transition.
What you need in the rounds are finesse. You can get over the jumps and you have a nice pace. LOOK for your turns before you make them. I had no clue what fence you were going to till you were a few strides out. On the center lines, you should be making a straight line from rail to rail, not and s shape unless it's a severely broken line. If you have a fence off the rail come off the rail approaching straight. Don't ride the rail, then swerve out to that fence then back to the rail.
Between lines it's all about having a solid leg and hand. To me it looks like your horse dives for the rail. So block her with your outside leg at take off, so she is less liable to dive. Dressage or riding center lines can really help with straightening you out.
And one more thing... Elbows. Please unlock them. They are stuck out and your hands glued to your horse. It' looks pretty to some extent and helps your release, but gives you less control and communication. Very important for a green horse.
Once you smooth out your lines, I think you'll be unbeatable. In which case I will be avoiding the shows you're at. ;)