Lots of good suggestions here, I'm going to add one more -
If the rider sets their arm or pulls back as the horse rushes, you set up a cycle - more rushing, more pulling, more pulling, more rushing.
If you use trot poles or a ground pole in front of a fence, it's very important that the rider do as little as possible on the approach. Put a little loop in the run and if the horse wants to rush, that's fine. Let the poles and the gymnastic teach the horse to back off, rather than the rider. (Because if the rider asking worked, we won't be having this conversaton. )