I'm not sure what you did wrong, if anything. This is another of those problems where a cut and dried answer won't cut it. However, the rest of your letter says this has been building for sometime. I feel especially compelled to tell you up front, based on your relative lack of experience, to be careful with this horse. In my opinion and observation, for what it is worth, Appendix Quarter Horses, in an extremely high percentage of cases, require rather experienced riders.
Quarter horses are slow-twitch fibered horses.
In other words, they are bred for economy of energy. TBs, for the most part are bred for flat out speed over greater distances. In other words they are bred for expending energy. When Quarter Horses are bred to TBs you are breeding a slow twitch horse to a high twitch horse and these two qualities often war with each other. Predictability and rationality is not the Appendix's strong suit.