An exercise that helped me and might help you reach your goals is part of the warm-ups done in Chirioku karate. After straight high leg swings, ten each side (I seem to be the only person in the entire ma world that calls them can-cans) - the same warm-ups that are in lots of styles, they add a turning move. As with the frontal leg moves, the leg isn't kept rigid straight, but allowed to relax and be near straight.
It's done both sides. First, with the left ahead in a shoulder width stance pivot to your right, keeping the feet on the ground. If you started at 12 o'clock now you should be facing 5. Swing the right leg back. Keep the body bent at the small of the back. The most common mistake is to arch the back, which is shitty posture for back kicks. To emphasize the posture I often try to look under my right shoulder at the right foot as it rises. The foot returns to the ground, remaining in 5 o'clock position, then pivot back to 12 o'clock. Once that feels OK, then do the move the slightly more advanced way. Start the move with the left foot moving to the right, across the line of the right foot enough that when you pivot you are in stance facing 6 o'clock, then as the right foot returns (and you're still facing 6 o'clock) move it to the left so that when you pivot you are lined up to 12 o'clock again. They repeat ten times each side, every work out as part of their warm ups. This is a type of dynamic stretching (I avoid static in general) and for me, it helped learn to balance and keep good form. It does involve a little shuffling as to avoid moving sideways across the floor.
I count my kicks on the bag to avoid "cheating" and shorting the awkward side. Everyone had a better side, that's what you are working against, so to speak. I do spinning hooks and wheels as part of my warm-ups, also. They are good full body moves. I was taught to throw a left hook to start the upper body in rotation for the right leg spin kicks and vice versa.
Clear as hell? Well try it and ask questions if you wish.
This is part of their warm-ups and after a couple months in their class I realized that my spinning back, spinning sides, wheels, and spinning hooks worked better and smoother. The advanced people do it fast and keep their balance well. At one time we were doing these on soft gymnastic mats and that increased the difficulty. Maybe do them in sand.
Another exercise is to do a roundhouse (R) then follow with a spinning hook with the L, and this you can do continuous, and of course vice versa. What you are looking for is proper form so that the body is balanced and the kicks are focused.
Combine the air moves with bag and pad, of course. Doing spinning heels or hooks on a moving big bag is a good workout.
While these types of kicks are often low probability techniques, they have been used in the UFC (David Loiseau wiped out Charles McCarthy with a spinning back kick to the liver/solar plexus in their 2005 UFC fight) and there's a famous video of Andy Hug in K1 ending a match with a powerful spinning heel that smacks his opponents thigh like a sledge hammer, the poor fucker just drops in shock.
*edit* One common problem is "blind" kicking. It is usually good practice to watch you kicking foot. And don't try to look over your shoulder or the back will be arched, to say nothing of the awkward neck twist.