At the start of work with Warrior Pose, Virabhadrasana I, it's more important to keep the pelvis square than it is to get the back heel to the floor. Why? Because having a balanced platform from which to lengthen evenly into the backbend-like action in this pose will help to avoid straining the lower back.
The tug-of-war between hips and heel is caused by shortness in the back-leg groin. The short-term solution is simply to elevate the heel on a wedge or practice with the back-leg heel against a wall.
In the long term, you need to lengthen the groins. Here's a good exercise: Kneel facing a wall, about two feet away. Step the right foot forward, bring the right big toe into contact with the wall, and slide your left knee back into a comfortable lunge. Keep the right knee straight over the heel, and rest your hands on your hips. Are they square? For most beginners the right hip will be higher and the left hip farther from the wall. Press your hands into the wall. Drop the right thigh as you lift the left hip up and forward; at the same time, resist the left thigh away from the wall. Release the tailbone down and forward (toward the pubis), and raise the rib cage off the pelvis, lengthening the lower spine.
Gradually, as you lengthen and open your groin, you will be able to bring your foot closer to the floor in Virabhadrasana I, without shaking your hips.