I agree with tinyliny about getting out into the open to play. I cannot count how many dressage riders at the lower levels ride with their horse behind the leg. Without forward, there's nothing to collect when you finally get to that point. Riding in the open will build muscle and give you the missing ingredient of forward without much effort.
To me it sounds like your instructor was simply teaching you about contact. Nothing wrong with that. After rhythm and relaxation, the next step on the training scale is contact, not to be confused with collection. Proper contact is very important. Sounds like you're off to a good start. Dressage is very addictive. Have fun!!
Do not be afraid to use a whip if needed. It is only used to emphasize your leg aid, not as a punishment. Use it behind the leg only after asking with your leg first, and the horse will become sharper to the aids.
I like what I hear you say about your instructor, it is important to right away begin to understand contact, for you & the horse. I like to explain contact as a living communication with your horse, without contact, the aids are unclear. It is also good that she will get on your horse to show you something or to check on the horse's response. Very good!
If your horse was a western horse, if may be used to going slow and without suspension. Wake him up & get him moving. It is better to see a horse going a bit too fast than puttering along. Quarter horses tend to do well warming up with lots of canter work instead of trot. It helps to soften & loosen their back.
Go to shows and watch the upper level riders to see what you should aim for. Always tape your lesson if someone is available to do so, you can rewatch it before your next ride to help you learn. Often times I understand what the instructor is saying by watching myself ride while listening to the instructors comments & instructions.
Dressage is a great sport because you are only tested on what you have learned & acomplished, not in comparison to anyone else.
So much of our riding is in the hands. If you want to increase your game in a hurry. Start working on your upper body strength. If and when you get tired your riding will suffer. Tired arms and hands are hard on horses mouths.
That's an interesting comment, about working on having good upper body strength. I have to agree with that. One lesson I had, my teacher said that to have a good upper body position and frame from which to have a steady hand, one should have some portion of the upper arm behind the middle of the torso, maybe even behind the back and kind of tighten the muscles in the arm pit area, of all places, as if we were trying to hold a $100 bill there throughout our ride. Helps to keep the collarbone open and the upper arm vertical. It takes activating muscles and will tire you after awhile.
Totally off topic, and not meant to highjack a thread, I wish someone had told me to strengthen my upper body befor my baby was born. You'd be surprised how tiring it is to carry an 8 lb. Baby around nearly all day.!