I practice balancing on foot off the ice, in standing and shoot the duck positions (maybe I should practice in between too...) and observe how I shift my body to do so. I think most people use a variety of techniques to place their center of gravity over their foot, and what I have to do on the ice is fairly similar - though during spins and some other dynamic balance moves, your center may be substantially offset from the base of support, in part because of the skating standard that most spins should progress around a small circle while on edge, and in part because the physics of balance changes while spinning.
But different coaches use hips in different ways. Some stick the hip slightly to the outside, some slightly to the inside, and some work hard not to let the hip line of the standing leg be visible at all. Many people seem to find some way to place the standing leg slightly outside the center of support, and rotate their pelvis upwards from the standing hip joint as well.
BTW, I've been told in the past that the leg should be parallel to the other leg as it passes it, but should rotate outwards at the leg/hip joint when behind and in front of the body. Some coaches have allowed some of the rotation to occur at the base of the spine or within the spine, but not all. One coach spent a lot of time having students work on practicing off ice to do many types of rotation just using the leg/hip joint. It's really hard, and takes a lot of practice, and I sometimes don't realize I am moving something else.
Many ice dance coaches advocate using what rotation they can about the ankle, and some a little rotation about the knee as well. Some are more worried you will be injured by too much such rotation.
Standing on one foot off-ice for an extended time also helps me strengthen the muscles needed to hold these positions. Perhaps, unlike me, you are too fit to need strengthening (but strength helps you fight flexibility limits too), but merely need to concentrate on doing the right thing.
Maybe none of this applies to you. Ask your coach!