To summarize my coaching for shooting off the dribble is:
(1) Catch the UpForce or Leg Drive. Shoot powerfully from the strong, stable force of the legs and middle body! You need it more than ever, with all the variables of movement when shooting off the dribble.
(2) Get aligned as well as you can quickly, but then "let go," trust, and fire the shot off. Don't take the time to get exactly aligned as you do with catch and shoot and free throws, especially when moving toward your strong side. Just get the center of the hand (the palm) in pretty good alignment with your shooting eye and the basket to help ensure accuracy! With movement left and right, it's not possible to be as aligned with the shooting eye as with a free throw or standing jump shot, so you have to do your best and then pull the trigger. For right handers moving to their left (vice versa for lefties), alignment and an open body position is easier, it's there instantly. But when going to the right, you probably don't have the time to rotate all around to be "open" to the target as you've learned. My coaching is just to turn as much as possible, get as "aligned" with the palm, shooting eye and target as you can, and let it fly! "Catching the UpForce" and having a great Follow Through are more important than getting the body aligned just so.
(3) Have a powerful "Finish" to the shot. With your constant and automatic Release, have a Follow Through that is powerfully connected to the basket. The ball will then fly true toward and into it. A strong, quick Release with a powerful and connected Follow Through will make up for all the movement and chaos.
The UpForce at the beginning, the automatic and "full-out" Release in the middle, and a great Follow Through will get your ball flying true to the target, high and soft. Repeatable.