Try sitting trot at a SUPER slow trot without stirrups. It should be so slow that your horse could break into the walk at any moment. Think about your hips going side to side and just let your legs hang. Sit back almost exaggerated, too. This should cause your seat to deepen, making it easier for you to ride.
Once you have that down stirrupless, try the same thing with very long stirrups. You can gradually raise them.
I am also a naturally tense person, which causes a ton of problems in my riding, you just have to learn to push through and try different things to help you.
Good luck! :)