You raised a lot of points to discuss here and I am sure many ski instructors will respond appropriately. I am NOT a ski instructor but I have three children who have been skiing for about 9 years now (since they were 3 or 4) so my opinions come from someone who has seen how kids skiing progress.
You mention that your son sits in the back seat and fights to get the skis to turn. Based on this, without even knowing what equipment and length of ski he uses, I could only say he needs more ski lessons. From experience, new or better equipment does not necessar make a kid ski better, especially if their technique is wrong to begin with. Many will disagree with me on this, but my disclaimer stands: I base this from experience.
One of my daughters is also 12 years old but she has been skiing since she was 3 years old. She is 5'2" and weighs only 93 lbs. Although she is a really skinny and light weight kid she can ski long or short skis. I buy various length youth skis that I collect to save on rental fees. Sometimes I let her ski 143s (her own K2 Superstitious) and sometimes I let her ski 153s (her mother's K2 superstitious). Of course, she can tell the difference in length but can immediately adjust her technique. She has funky wide feet so we let her try on different kinds of boots (her mother's and her sister's) and with different boots she can also appropriately change her ski style. Regardless of ski and boots, her skiing technique is basically still good (in all modesty.)
All that technique was learned from six years of ski school in every single resort we have been: Whistler, Park City, Deer Valley, Killington, Canyons, Hunter, etc. etc. At some point, she got tired of ski school and just wanted to ski with us.
So in summary, without knowing your kid's equipment, it is his technique that is "holding him back" and not his equipment. I suggest you enroll him in a Park City ski school, and let the school suggest what length skis he should use.
My five cents.