Great video and great to see kids skiing and having fun together with the rest of the family. As once a professional ski instructor (now half time) and a father of two boyz I have a good hunch when it comes to kids and skiing.
My first advice, forget about teaching her parallel skiing. Since you have allredy started with a wedge, which by the way IMO is the best way to start, she is for the time beeing stuck with it. And thats good. She can turn and she can brake. She can also ski from one location in a ski resort to annother. Most importantly, she learns how to balance, edging and pressure controll. Lets not forget that she has a lot of fun. Now you want to take all that away from her!
My second advie would be for you to forget about teaching her how to ski with parallel skis. Have her learn how to carve insted. Carving will give her parallel skis. Inside ski will be drifting but she has the rest of her life to get it carving.
My third advice would be fine tuning equipment. What snowbowler said, get her shorter skis. Chin hight is ok. 100cm modern kids SL kind of shaped skis are great. Preferably with some kind of plate. Marker makes good binding and plate combinations for kids up to 40kg. It makes a huge difference. Get her comfortable boots with a proper fit and dont listen to your whifes wining about the 3 pair of socks needed to prevent your princess from freezing her toes off.
Forth. Note that all kids are in the back seat. What you should do though is calm her upper body down. See those windmilling arms, hip rotation, banking, wobbling for aft balance etc? All that you can fix easily with one simple move, let her put her hands on her knees or upper legs for a more upright stance. Ski in front of her and have her follow you on easy terrain. Go faster and push her wedging limits. Make me a new video and post is here as a follow up. If she shows no progress you can have your money back
Fift, get her into weekly lessons over a longer time period. Private lessons are not much bang for buck since she allready skis well enough to outski most kids instructors
Have fun, tdk