Two reasons for the lack of confidence.
One: The feeling catching an edge. When you are using your back foot to pivot the board you need to keep the board fairly flat to the ground when changing edges. The flatter the board the easier it is to catch the edge, but the faster and easier to pivot the baord around.
Two: Feeling like every bump is going to knock you over. This is feeling is from two specific thinks. One. On your toeside your shoulders are open a little wider than they need be to the nose of the board. This cause your spine to twist up and your front leg to straighten out, leaving most of your weight on the back foot. because you need the board to be fairly flat to pivot you are creating tilt in the board by leaning your whole body. A straight leg can't absorb bumps, It is hard to maintain balance on one leg, and when your weight is out past the edge of the snowboard you have to work harder at maintaining your balance.
There would be two exercises I would work with you first on.
One- Rotation. We would start by getting our body to rotate and be aligned in the direction that we are turning. Two steps to this. First would be to practice rotating our hips by envisioning our knee out over our Big toe and moving out and around to the little toe for toe to heel. For heel to toe the knee would go from out over the pinky toe to out over the big toe. Second, with our hands on the toe side have our lead hand rest on the inside of our front leg and the back hand on the hamstring/outsidebutt area of our back leg. Then when turning to the heels the hand should move to front hand on front leg hamstring and back hand on inside of back leg(as if you were goin to scratch your nut closest to the back leg). This should help keep your body front should/hip/knee/outside of front foot always pointing in the direction you are trying to make your board go. It will also help you to be aligned to be able to keep bend your knees evenly and not have one that is forced to be staighter and the other to support more weight.
Two- we would work on progressively learning how to tilt our board edge. First with both feet and then by seperating the feet a little bit to get a one, two feeling. To do this we first would start with a j-turn on steeper green. Startout with the board flat and nose pointed down the fall line. Next, with your ankles followed up by levering against your highback, think of increasing the angle of your board with the snow5-10 degrees at a time. one way to envision this is to think like you are ratching your bindings, at each click you flex your ankles up an or lever your hi-back a quarter of an inch. Start with ankles first and then the levering. Try to not make a full body lean. To assist with not leaning up the hill as you ratch your ankles up, you will release your knees down(i.e. bend your knees MORE; this should feel like you are lowering your hips down toward your heels. Half way through your j you the Big toe to little toe movement from above to help round out and finish your j-turn. Next try this on toes by starting out on a flat board. Bend your knees out over your pinky toes like a cowboy straddling a horse. Feel your butt scope underneath your hips and your hips push forward while slightly arching your back to keep it upright. This will help position you out over the toes. Next try to bend your boots a little at time by lowering your knees and hips down. After starting to make this movement start to extend out your ankles by pushing down on your toes and raising your heels(i.e. standing on your toes like a ballerina)... Make these move similiar to the ratcheting you did on your heelside. About half way through make the front knee rotate from over the pinky toe to over the big toe. Don't forget your hands
to help make sure the rest of your body is following suit.
After getting this down try starting the movements with the front first and then use the back foot.
Next step is to smooth out the ratcheting and incorporate these movements into your riding. This is jsut the start. Be sure to look through finishing your turns and not getting caught starring straight down the run. This will cause you to block your spine and prevent your lower movement(primarliy the rotary movements from being able to finish out.)
P.S. By the way for only 7 times with out lessons you are looking good.