First of all, I'm glad that you had so much fun at your hunter pace! Those are always so much fun and such a great experience for both horse and rider. And they are getting harder and harder to find, unfortunately. I'm glad you have access to one! Now, onto your question!
I think you will find all of the answers that you are looking for in this article on the horse that drifts when jumping. But there is something that I also want to mention that shows up in this series of photos.... (Click on Photo/Question Title above to read the full answer and critique of these photos.)