Practice the piqué movement without the turn. Make sure you are stepping smoothly onto a straight leg without hopping onto the foot. Once up on relevé, be sure your hip adjusts so it is centered over your foot, out to the side. This helps you keep your balance by bringing your center of gravity toward the midline of your body. As you slide the passé leg down behind, remember to keep it close to your other leg. This will help keep your turns on a straight line.
Add the turn back in, going very slowly at first. Make sure you are spotting, and if you haven't already done so, put up some blue painters' tape on the wall in your practice space to give yourself a good point on which to fix your eyes as you spin. As you turn, remember that the turn is actually only about three-quarters of a turn. It is very easy to over-spin and end up doing your piqué turns in a curving arc, rather than a straight line across the floor. Think about getting the passé leg ready to come back down before you think you need to.
Gradually speed up your turns. If your posture or anything else starts to deteriorate with speed, slow back down. Go back to practicing piqué without a turn to refresh your muscle memory on what that feels like. Work through your whole range of speed, from no turn to very fast turns, until your movements are consistent and balanced regardless of speed.