If you're bi-laterally loaded (moving while using both hands and/or both feet), naturally your body is moving straight. If you want to turn while bi-laterally loaded, you have to create rotation. But if you're uni-laterally loaded (moving while using only one hand and/or foot), naturally your body will want to turn - typically towards internal rotation. If you want to move straight while uni-laterally loaded, you must resist rotation instead. We've hit on these concepts before with the one-arm push up and pistol, and here is another bodyweight movement to practice core stability under uni-lateral load.
In this video, Carl demonstrates how to use the tripod headstand as a foundation for a uni-lateral movement. By picking up the legs and twisting the lower body while in a headstand, this is a great movement to strengthen your core stability while transitioning with rotations. The next level of difficulty would be to touching opposite knees to elbows, which would help build your motor control and body awareness to skill transfer to other movements such as pistols and sports-specific skills.