I definitely think it would be a horrible idea to just give up and use your "weak" hand instead.
If you were a client of mine, I'd likely recommend starting with a big movement the shoulder was designed to do, and that is the press. It wouldn't matter if you were just starting with PVC - just start getting accustomed to the range of motion in small increments as best as you can. The press is a incredibly safe movement that the shoulder was literally designed to do, but doing it correctly is an absolute must. When done correctly, there is remarkable gain in function for people with severe shoulder injuries.
If you are interested, I can link you to information explaining the movement in detail and possibly places for personal coaching.
Remember, rehabilitation stops when the joint/muscle is as strong or stronger than before the injury.
The bottom line is, the human body is best rehabilitated by doing the movements it was originally designed to do.