One way to address dysfuntion at the hip and shoulder is to fix the pevlis and scapula. Improving pelvic and scapular stability will give the muscles, which dynamically stabilize the bones of the hip and shoulder, a mechanical advantage. In this way, glute activation, hip extension patterns, and scapular stability exercises all play their part.
Another way, which is most commonly addressed at the shoulder, but not the hip, is to improve the functioning of the smaller, deeper muscles, or the rotator cuff. The hips need mobility, but stretching and soft tissue work won't suffice if the muscles that center the head of the femur in the hip socket aren't working properly.
I posted a video of a hip-rotator band series. There are many versions and variations of exercises to strengthen the hip rotators. I like the way these flow, however, it's important to know that they are a progression or two beyond 1) not using a band, 2) using a lighter band, and a progression before integrating them into a standing version.
Side lying exercises, and hip bridges are good place to start before using the progressions in the video.