As a beginner rider with 7 lessons under your belt, I think are putting too much pressure on yourself. Becoming a great rider doesn't happen overnight. I have been riding since before I could walk and still 30 some years later there is still always something I could work on or do better. Set small achievable goals, each of those little ones that you check off lead up to the big picture. Don't worry about other riders. What they are doing isn't going to help your riding. I know that's easier said than done but really try to focus on yourself.
As far as the horse goes, sounds like a typical schoolie that is testing to see how much she can get by with. I have one like that. I usually start riders out on my mare that does whatever any level or size of rider asks to learn basic control, cues, finding balance. Then they move on to my "tester" to learn how to be the boss and make her mind. She doesn't do anything bad, just typical aged lesson horse tricks like trying to come to me or a gate, trying to get out of work because she thinks she can. Once her rider shows her they have the upper hand, she won't try it again. Ask your coach for guidance on how to become the mare's "boss".
Sitting the trot - toughest thing to learn. Think about being a "weeble" - the kids toys that wobble but won't fall down. They work with a metal ball bearing inside that rolls with the motion to keep the toy centered and balanced. Think about having that ball in your midsection, letting it move freely to absorb the shock of the horse's movement instead of your rear end. We expect our horses to move each body part independently, we as riders need to as well.
Life is like a camera. Focus on what's important, Capture the good times, Develop from the negatives and if things don't work out, Take another shot.