There is no easy answer to this I am afraid, since getting the CM moving inside and in front of the turn (in the direction of the next one) requires coordination, balance and timing. So let me point out some of the things people do that tend to prevent them from going "lateral" in order to get to the things that will get you lower.
a) Passive skiing: any type of skiing that is passive (ie. reacting to the forces once they've thrown you out of balance, rythmn, etc.) will prevent you from moving the CM down the hill and into the turn. This can cover a broad range of issue such as lack of upper/lower body separation, incorrect fore/aft balance, banking, etc. I see aggressive skiing not as being aggressive, but as being neutral: you can do anything you want anytime you want it because you are in a position that allows you to do so (ie. the CM is always moving downhill from one turn to the other).
b) Lack of early edge angle: wether we're talking about asymetry or incorrect pressure or anything of the sort. The skier who can go inside will be the one who is patient, yet proactive in his transition. While using the g type turn, it is my belief that both crossover and crossunder should be used, wich means a very strong down unweighting motion (one of the key aspect of a successful transition since it will put your legs in neutral and allow them to exchange role (outside/inside) quicker and more efficiently. I see a lot of coaches telling kids: "get your outside leg small at the end of the turn" or "get your inside leg long" while, in reality, they should say "get your legs in neutral and then make them switch role". Inclination should also begin as soon as the down unweighting phase is finished in order not to stop the flow of the CM from one turn to the other and to tap into the "torque" produced by the counter rotational movement of the upper/lower going into the new turn.
c) Lack of continuons movement: a great coach once told me to ski like I would if I was runing from a lion. Why? To keep me moving, because once you stop to run, you're dead. A lot of people when they think go lateral will throw themselves at the mountain or try to muscle their butt into the turn and then will wait for the ski bend and sidecut to carry them through the turn. The key to getting low is to continue to get low in the fall line and to finish the turn at your lowest. Many times I've seen capable skiers who give it all as soon as possible and end up stalling their turn. Be patient, the first phase of the turn should not be botched as a successfull entry into the turn will yield a more stable platform due to the CM being just in the right place to counteract the forces built up by the increased edge angle than if you try to get too low too soon.
d) Correct alignement of the ankle, knees and hips. Many people will rotate the hips in order to start the turn in the hopes that this will get them more inside movement. While this will work to initiate the turn, it is a very poor maneuver. Try it at home. Stand on both feet and rotate the butt. See your feet lifting ever so slightly? This is as much edge angle as turning the butt will get you. This move also puts the outside ski farther away from your bigger muscles and makes pressuring it adequately even harder. It is my belief that a VERY STRONG commitment to the outside is necessary during the race turn. This is not to say that the inside ski doesn't have an important place, not at all, since it should also carry some weight in order to inscrease its bend and carve. How much is dependant of the turn and tactics. So, avoid rotating the hips and inside use your waist to get "into the turn". Breaking at the waist should happen once you get to the second phase (fall line) to prevent "falling" on the inside, to keep pressure on the outside and to increase upper/lower separation.
So, some drills:
a) Forceful down unweigthing. Try to hit your face with your knees.
b) Footwork (skiing without poles, skiing on one ski, skiing on the oustide ski only, etc.)
c) Forward pole plant. This is especially important. I always advocate a double pole touch in gs for any terrain that isn't flat. If you aren't tucking it, you should be planting it since it will make the down unweighting phase asier and sill tend to prevent going Wbackset". But always remember that you should initiate pole plant with the WAIST. This is somewhat strange, but remember to pull the waist first to prevent you from only hunching and staying in the old turn.
d) Roller blade carves. These are really good for edge pressure and control. Try to mess around with the first phase of the turn. Make it very quick or very slow. Increase or decrease edge ankles using the ankles during the turn, etc. The last exercise is especially good and will show you how it is important to use the ankles and not just the hips at initiation by how much angle you'll be able to get.
e) Double pole plant on the inside of the new turn (normall called the Norwegian pole plant). This insures that the CM will go downhill after a neutral period. Also aids in the simultaneous movement of the feet since it will force you to let go of the ouside pressure of the new turn.
PS: I have seen many skiers not being able to get inside because their boots were too stiff laterally for them. Yep, you heard me right. This is why the Solly had all the little holes: to facilitate inside movement. Make sure that you are able to flex the boot to the inside and not go A frame since the leg shaft ski boot/ski interface should always form a 90 degrees angle.
Whew, that was lengthy and probably not a whole not more instructive than what you were used to, but at least I tried