It's great that you want to progress and there are already some excellent tips. I'm no ski teacher, but I have been taught by some great ones and here are a few thoughts and some suggestions for things to practise that have helped me. Of course, without seeing you ski I can't tell what applies to you, but the things I mention below are pretty general.
Modern trails are groomed like highways so it often comes as a shock to find yourself in uneven snow. The general truth is that if you have a good technique on the easy stuff it will work on what's difficult. But, on the other hand, the combination of groomed trail and modern equipment will let you get away with a lot. It's only when the going gets tough that you get found out.
One common problem is that skiing is a matter of what I call "reactive strength". It's not about consistently applying huge forces to the snow with your legs (unless you're a racer) so much as being prepared to absorb what is thrown at you quickly and smoothly. Just being strong in the legs doesn't suffice -- in fact, it can be a handicap if you're tense.
The best way to promote this is just by skiing uneven terrain. Find some uneven snow (mini-bumps or an up-and-down traverse) and simply ski it straight, concentrating on relaxing, breathing and absorbing. Unfortunately, this is one of the most difficult (and scary) things for adults to learn -- it's remarkable how quickly kids get the idea -- but it IS important.
Sideslipping is one of the things we learn as a kind of safety net -- if all else fails, sideslip! -- so there's a tendency to think that, once we have the confidence to turn on steep slopes, we can leave sideslipping behind. But actually sideslipping is a great drill to practise: if you can do it well, it will benefit you in lots of other ways.
The first thing to note is that good sideslipping involves "releasing" (that is, flattening) the skis. That, believe me, can be scary -- no one wants to catch an outside edge and end up head first on the snow -- but, if you can overcome it, it will give you an experience of "flowing" that is incredibly liberating and leads to all kinds of other good stuff (the next stage is a drill called the "pivot slip", discussed in the technique thread -- if you can do that well, you don't need any advice from me!)
Apart from teaching you to release your ski, sideslipping also teaches you about weight distribution. In order to go straight down the hill rather than at an angle your weight must be in the middle of the ski, so, if you find yourself going forwards or backwards as you go down, you should adjust your balance. It should also teach you to lean your weight outwards, not in to the hll (another scary thing) to get a smooth flow.
You'd be surprised how many fast and confident skiers can't sideslip!
Upper and Lower Body
Another very common weakness of skiers who get by really well on the groomed trail but have difficulty when the terrain gets tougher is that they don't "separate" the upper and lower body. It's very difficult to describe this without getting in to a lot of technical language, but it's really easy to spot when you see a skier on the hill who has that separation: he/she just looks so much more relaxed, elegant and in control.
I was once given what I thought was an excellent drill to help this. Bend your arms at the elbows and, with the upper arms against your torso, point the forearms in front of you, with your palms open and facing one another and the thumbs pointing straight up in the air. Using the flat, upper part of your index fingers as a rest, put your ski poles across your hands. Now start skiing down the hill with the ski poles resting there, trying not to lose them as you turn. The idea is that, since you're not holding the poles, you have to keep your hands horizontal, which will (should!) force you to move upper and lower body independently.
One of the things I notice about myself is that, in trying to relax as I ski, I'm sometimes too upright. Here's a great technique someone showed me to try to get me to correct that.
Stand static on the hill where it is reasonably steep with your skis on edge. Take your ski poles in each hand, holding them as if each were a sword you were going to poke. Have a friend stand a couple of feet below you with his/her body slightly in front of yours. Have them grab the basket ends of your poles and try to pull you downhill. Your job is to edge and pull back. You'll find that, as you pull back, your legs bend naturally, your hips turn and you apply force with your back by bending, not crouching. I call this a "power position". It's a great position to ski from and encourages naturally something that the pros call "angulation" of the hips, which is hard to describe in simple terms but is another GOOD THING.
P.S. As I said, I'm not a ski teacher (Rick, on the other hand, is -- and a terrific one) and I'm putting this stuff out as something that has worked for me in a similar situation. If it doesn't make sense to you, I'm sorry -- good luck in any case!