When you are riding, think "belly dancer!" You are going to have to try some very awkward exercises, so don't do them with anyone watching!
Your hips need to rock and flow with the horse underneath you, meaning you are isolating your core and relaxing your hips to rock them back and forth.
On my college team we called this the English-Western exercise, ha. While standing, bend your knees slightly and pretend you are on a horse. For a moment, ride "Western:" draw your pelvis up through your belly button and tuck your tail bone, almost like you are "pelvic-thrusting" into the air. Then, ride "English:" arch your back, stick your butt out, but maintain your posture. The key
is that the whole time, you are holding your shoulders and chest steady-- they shouldn't move! But your hips should swing forward and back, using your core strength and your lower back muscles to control the movement. The slower, the better!
This is an exaggerated movement, but helps you understand what it feels like to have your hips swing free while your upper body remains still. It's also pretty hilarious.
ETA... if you are not talking about relaxing your hips with your horse's movement, but actually stretching tight hips, I agree with taking a yoga class once or twice a week!