The horse my daughter rides is super bouncy,her back moves five inches when trotting, and also is super fast when in heat. Because there is bouncy, you don't necessarily need to post but more like go up when her back pushes you up. As my trainer says, let the bounce post you, not you post the bounce.
First, try riding stirrupless or bareback. This will give you needed leg muscles and a better sense of balance. When trying to go slower, give outside half halts and sing a song that has a slow beat. When the beat hits, rise or fall with your post. And breath, the more you relax the easier it is to ride.
The way my daughter was taught to keep her hands steady was having her hands by her withers, almost holding on the the saddle pad. After three months of this her hands learned to be steady and she was soon ready to bring her hands up in a true dressage hold.
Hope this helps and talk to your trainer!