Here's an easy-peasy solution for getting wedgers to wedge christies. It's worked for me in never-ever lessons when things are going right.
Once everyone has gotten turns going with their wedges on the slow beginner terrain, I stop them all and explain that the outside ski is turning them, and make sure they feel the extra "weight" on that outside ski. If they haven't yet felt that, we take a half run and feel for it. I then get them to realize that the outside ski takes them in the direction it is pointed, and that the inside ski, not pointed that way, scrapes agains the snow and works against the turn. If that doesn't work, I use "thumpers" to get them to move that inside ski's tail over. If they seem to understand the power of having both skis pointing in the same direction as they finish the turn, I get them to increase the weight on that outside ski, while decreasing the weight on the inside ski, progressing to having them lift the tail of the inside ski and hinge it over and set it down to match the outside ski as soon as they can. Once skis match, they are using both skis to turn, and since turning is how they stop, they've got both skis able to help them stop or slow down. We make a half run or so moving the tail over in the air, then by sliding it over. This takes care of the end of the turn, but not the initiation. IME about half of them won't go back into the wedge at all once they get onto the next slightly steeper trail (AKA "Spontaneous Christie"). The other half will need a direct focus to get a parallel initiation going.
For a lesson focusing entirely on getting wedgers fully to parallel, I have several ways I do this.
1. First choice: "flamingo turns." Lift the tail of the new inside ski and tip it to its Little Toe Edge while heading down the fall line, facing the upper body down the fall line all the while. Athletic skiers can do this. Then I have them stop lifting the tail and just lighten it. If that clicks, I have them transfer this lightening and tipping to slightly wider turns. If there's time, I have them add pulling-back the lightened, tipped inside ski. Dramatic change for the better; turns get sharper and more powerful. The first student I ever had do this was the star newbie in a British group of teens. She did an unexpected flat 360. After dusting herself off, she continued with very strong parallel turns. The rest of the group followed suit. The goal is for the skier to lighten, tip, and pull back the new inside ski for a flex-to-release turn. Pressure comes to the new outside ski as the turn progresses. This is a flex-to-release turn.
2. An alternative: I call this "drop the hip." I've actually done this in a newbie lesson successfully, but it's better in a wedge-to-parallel lesson. It has only worked if the student(s) have skiing-into-counter first. I've taught that, then followed with this. I've had more success when I don't have to teach both unfamiliar movements, though. Skier makes turns on a steepish run, focusing on skiing into counter, and holding that counter through the entire transition, making wedge turns. Then I demo and have student do one turn at a time, cruising uphill to a stop, this way: I have them imagine a taut wire stretched vertically from their new inside foot up to the interior/middle of their new inside hip (downhill foot and downhill hip). Their goal is to push off parallel, in a traverse, and lower that hip by sliding it down that wire towards that foot. I demo statically, while we stand there, and have them try it statically. Then I do one turn. They follow. We do one turn at a time, in both directions, until it's working and they can affirm that they understand. Then I send them down linking turns. Works like a charm. Pole plants go in afterwards and they are doing flex-to-release turns.
3. Another alternative: I discovered this one in a video by Rob Butler, a LIV CSIA guy. This is an early, assertive engagement of the new outside ski. Between turns, skier heads across the hill after having rotated/slid the old inside/uphill ski tail over to match the outside ski. Then, to start the next turn, the do not go back into a wedge. They slide the new outside ski/uphill ski slightly backwards, relative to the hip above it. That leg before the slide-back is flexed, but as they slide the foot/ski back, it lengthens. It starts out on the LTE, and as they slide it back, it tips onto the BTE (big toe edge). The turn starts, and they don't even have to think about what happens next because it's embedded in muscle memory. The turn will be parallel all the way. This is an extend-to-release turn; pressure goes immediately to the new outside ski as that foot moves backwards behind the hip above it. See the video here: https://www.youtube.com/watch?v=Rba2rQl-cWk
There are a few others I've used, but I'm getting too long-winded so will stop there.
I belong to the do-what-works camp. These three options may not satisfy some PSIA trainers, but they satisfy my clients. And they don't teach the skier anything they need to get rid of, ever.