You're likely freaking out because due to the steeper incline of the terrain, you're gaining speed quicker and must therefor initiate turns quicker (as well as more turns to keep your speed down and controlled). To get a better feel for the turn in without getting out of control, head up to the slope that's giving you trouble and try this: Start at the top of the slope on heelside and make your first toeside carve into the mountain. Make it sharp and come to a complete stop. Now make your heelside and once again come to a complete stop. By doing this you will get a better feel for the balance and torque the turn requires without gaining too much speed and having to bail.
One thing I can't stress enough about most things in snowboarding is that you have to commit to whatever it is you're doing. When you don't shit usually goes bad in your attempt to save it and a lot of injuries happen here. Applying the brakes after the turn is fine, but if you fail to commit to it you will end up pointing straight down the hill causing you to get more speed then you're comfortable dealing with.
Thanks alot, I'm going to give it a shot this weekend and see if I get a little more comfortable.
Otherwise I'm taking a lesson.