Enormous and difficult questions, Cosmic.
I don't know of any printed resource that begins to deal with teaching kids to ski. There may be one but I'm going to be very suspecious of it until I hear good reviews from some parents.
A good instructor, not a good book is my prescription.
I'm old enough to be entitled not to remember when and where I have said various things nor who may have been active on the board at that time. So here's a short recap of my ski and board background. Bill Koch League X-Country youth racing team coach; telemark instructor certified by EPSTI; snowboard instructor for 6 years, last two of which included instructor staff training and supervision. I've been involved in teaching my two kids and six grandkids how to ski, board or both.
My method has been to be the kid's first instructor because I have their confidence and am a familiar family member. In my opinion, leaving a pre-schooler with a stranger for an hour is not a recipe for progress. We just go out and have fun on the bunny slope, working just a touch of technique into the mix. In the case of skiing, as soon as the kid is comfortable going down a short easy green on his or her own and has accepted the idea that he or she is a skier, just like the rest of the family, we start building up the idea that skiers take lessons from pro instructors. Once the kid is eager for a pro lesson, we arrange a short private with a PSIA instructor with at least level II certification -- I'll pay a bit extra to be guaranteed a III. (Some areas want to just assert that they teach PSIA method or that all of the staff is PSIA and won't cooperate with a specific instructor level request -- go to a different area. A level I has been through area training, has taught briefly and has the PSIA syllabus memorized -- a level two has taught longer, has been through a PSIA clinic and knows why the syllabus is important -- a level III is life-long educator.) After one terrible disaster with a ski instructor-with-attitude at Mt. Mansfield who nearly turned my oldest granddaughter off on skiing for good, I have always insisted on meeting the instructor in advance and discussing the approach and philosophy of the instructor and making sure that he understood mine -- 1st: a good time is to be had; 2nd: a positive attitude is to be exhibited; and 3rd: a flexible approach, dependent on the child's learning style and enthusiasm from moment to moment, is required.
After the private lesson, I discuss it personally with the instructor and find out what was accomplished and what needs to be worked on at a level that I can attend to during ordinary, fun skiing.
Once they were into this learning curve, we generally gave them two or three privates a year and a lot of personal attention on the slopes.
The big problem is that kids have about ten thousand different combinations of ways of learning, responses to teaching, natural ability, length of concentration, desire to learn in general and desire to learn to ski in particular. And, of course, even within the PSIA syllabus there is a lot of room for interpretation and variation of method. A mature adult instructor with the teaching experience that leads to being one of the private instructors at a thoughtful arrea is going to be seeing twenty different one-on-one private students a week. That instructor is going to develop an intuitive feel for how to handle each kid. At most areas, if a customer requests a repeat lesson with a specific instructor by name, the instructor will get a higher rate of pay for that lesson. Believe me, a good instructor wants to please you by making your kid happy with the lesson and you happy with the progress.
(With respect to boarding, from my daughter-in-law on down, I have tended to be the exclusive teacher. I have writen a book on the subject of teaching snowboarding. Actually, its a manual for teaching instructors, taking the AASI sylabus and explaining not only each step but why each step is taught. It identifies the likely problems and describes the symptoms that such problem is developing -- then suggests ways of dealing with it. The manual was specific to my area and described specific spots on particular trails which were ideal for certain drills. When I quit and moved West, I gave it to my area as a gift for putting up with me for 6 years. For a while, at least, it was up-dated by the staff at the area but the version on my computer no longer represents state-of-the art thinking about certain aspects of boarding and will not be provided to anyone.
(In my personal teaching the number one concern has alway been adjusting to the student, not any particular technique or sequence of instruction. For example, my youngest grandson is now 7 and has been skiing for 6 years. He has resolutely resisted using poles. This year he was skiing off the true summit at Breck, doing Whales Tale, Georges Thumb, the 6-Chair area and two different sets of black trees. But, he skis without poles. You'll never find a book or an instructor (including me) that would advise this approach, but you'll also find it rare to have a skier of his age with such enthusiasm and eagerness to challenge the whole mountain.)
It's a process. The important things to remember are Bruce Kleerup's three rules: the second one is "HAVE FUN!" and the third is "Don't take yourself too seriously."
They go along with the North American Telemark Organization's motto: "Be safe, play fair, have fun."
And, by the way, good luck.