If you're struggling to hit fairways, put more emphasis on where the ball starts and less on where it lands. Odds are, if you start the ball on line, it will finish in the short grass.
Try this drill on the range: Stick two umbrellas (or broken shafts) into the ground several feet in front of you and on either side of the target line. This will form a "doorway" several feet wide. Try to hit several balls through the doorway without paying any attention to where they land. Once you're on the course, picture the two "goalposts" in front of you and try to split them with your tee shot. By aiming at a target that's several feet in front of you rather than one that's a few hundred yards away, you'll swing much more freely and release the clubhead more naturally. You'll also worry less about the trouble and what might happen if you miss, which should free you up to make a confident, accurate swing.
On the range, use two umbrellas or broken clubshafts to form a "doorway" a few feet in front of you…
…then take that image with you to the course to start splitting every fairway.