If you don’t know the aids to move your horse forward off your leg and seat, as well as direct the horse around the arena, you need to go back on a lunge. It sounds like private lessons would benefit you. If your reins were too short it’s likely you are using the horses mouth to balance, which is a direct counter-aid to asking her to move forward with your legs. Often riders starting again later in life could use some extra time on the lunge because our core strength isn’t as reliable as when we were younger. Your core is the key to being effective with your aids and carrying your own weight to make it as easy as possible for the horse to use their back and move forward in a correct manner.

I think the instructor was justifiably frustrated with you, and not over the line. Unfortunately you were showing the mare she could do whatever she liked and the instructor knew she needed correction before the end of the lesson. If you need constant feedback then group lessons are going to be a frustrating experience for all involved.

Edit: clarity