Once you have your elbow working correctly, add a shoulder lift. This is the second part to building a solid shoulder rotation.
When you understand how the body is designed to move, proper shoulder rotation becomes easy. This is why and how we hinge the wrist.
Proper arm rotation maximizes momentum into the ball, while maintaining path. Here is the first step towards getting your arms to rotate properly.
Each one of these skill pathways is a concept. When you learn each segment of arm rotation, adding a club to the sequence is not difficult.