Grew up righty doing the normal sports. Baseball, basketball, football, hockey, lacrosse, and soccer. Could not go to my left in basketball and threw very badly with my left hand. Did a bunch of work on it after starting on the work of Moshe Feldenkrais. It is not so much what I needed to do with the left hand to coordinate a good throw it is what I needed to contract on the right. The hand is sort of like the end of a whip. What I tend to do when trying to throw with the left is contract to early to generate the force. The left arm needs to extend back and wait till very late until the right pelvis trunk and shoulder contracts in a backward rotation forcefully and then the left hand arm and pec commits the throw. It is amazing to me how well I could coordinate the left throw until my sense of the situation demanded more than I could do easily. I would actually try to recruit the musculature to throw the ball with my right making the left throw impossible.
However if I would try and make the throw of only a few feet against a wall it felt pretty good from a coordination aspect.
Much of the work with the left seems to be short circuited by the right. "Here let me do it" the right side says.
"You'll just make a mess of it"