Ah yes, the hands shaking at the start of the lesson. Two or three possible helpful hints:
1) What the Lizard said - Warm up right before. If you can find a place to warm up that's quite close to your lesson, even better. In good weather, a folding seat and music stand (and some clothespins) carried in your car makes any parking lot a warm-up space.
2) Ask your teacher if you may play a warm-up piece before playing the challenging new material right there at the lesson. This is remarkably effective.
3) This does get better with time but for me it was more measured in years than months. Be patient with yourself.
