TPI has some good exercises and drills for learning how to rotate the hips independant of the upper body.
I think a good drill is just get to the top of the backswing, and then hold that position, then try to just concentrate on the left hip/knee bumping towards the target, starting that rotation.
I am in the same boat, i have a hard time getting that right elbow to drop down, it might be something i just can't feel in the swing.
If there is a wrong way to begin your downswing, there must be a right way?
Well starting the swing is individual. Some players might be like Jack Nicholas who lift there left heel off the ground, and replant it down. Some might bump the left knee towards the target, some slide the hips, so don't concentrate on the lower body at all because they already have a good action. So, how you begin is based on your golf swing and your own body, but a good golf swing is a chain of evens
Hips -> Torso -> Shoulders -> Arms -> Club
Now how you feel that happening is another issue