I also have balance issues with mine. I've had two different physical therapists who have worked on balance exercises with me.

My home health therapist stood me at our corner kitchen counter, slightly forward, then would 'push' me from different angles and the goal was for me to maintain my balance (all while safely strapped to the gait belt, of course).

My current PT does something similar, using my walker. They are slight nudges at best, but like you, I've had many falls and they're just taking their time. I'm still confined to the wheelchair at this point, but getting there slowly.