Welcome to the world of new "relearning" riders!
I know exactly what you are going through! After many years away from horses, I started riding again at the end of March- and have loved every minute!
I started out one horse(Dom), and of course, he had to test me at every turn, could barely get him to jog, then when he did, he would go around the ring halfway, then back to walk. He is not known for being stubborn, just wanting to test new riders.... after a few lessons on him, I moved to Suzie, a 12 year old Quarter Horse. For quite a while, she tested me at every single lesson. The very first time I got on her, she took off at a jog! I've been riding her every week, sometimes twice a week since the end of April, and it did take a while, where she wasn't constantly trying to tell me what we were going to do versus me telling her, lol!
Our riding ring is outdoors, and of course this time of year, all the weeds are high, nice lush grass, etc. Now, it only takes a slight nudge with my outside knee to keep her off the fence, and away from the grass. I have been putting her bridle on by myself for a couple of weeks now, it has got much easier, she is better at letting me, even unsure as I still am. I've been conciously trying to not use my hands as much when riding, getting more used to leg cues, which she is wonderful at, and that has been working out well.
But, if you think about it, it has really taken me 5 months to get to where I am with Suzie, I tend to have a laid back, sometimes unsure of myself personality, and I really think she picked up on that right away, and thought she would see what she would get away with. She is so good, and has also got used to the way that I ride. I will be going back to my original horse soon, Suzie doesn't lope, she is too rough, so I will be riding her one day a week, and Dom the other day. We will see what he thinks of me! He knows me, as I am at the barn usually 3 or 4 mornings a week, but riding him will be a totally different experience!
Hang in there with your lesson horse, I really sometimes wonder if they are testing us to see if we are going to stay loyal to them, or go with a different horse? 6 weeks is not long at all, before you know it, everything will click, and your girl will fall in love with each other!
Congrats on doing a show so soon, even though you were unhappy with the results, you will always remember that you tried it!