It requires more than Lito's book...Patentcad,
You can definitely teach your family member how to ski, but it requires much much more than Lito's book. For starters, you should pick up "Anyone can be an Expert Skier 1" by Harald Harb if you want to go down the path Lito is describing. The Harb book is much better at giving step-by-step lessons, though not as much fun to read.
Most importantly, you will need to get a significant amount of lessons from a teacher that fully understands the concepts you will be trying to teach. This is to make sure you are doing them correctly yourself, and some insight into a learning progression.
Prepare to spend hours upon hours of research and going over every movement analysis thread you can find in the instruction forum. Try to become familiar with alignment issues.
What you are trying to accomplish with all of this is an ability to spot inhibiting movements in other's skiing, and an understanding of how to replace it with an efficient movement. The biggest frustration you will have is when you are explaining a movement to your family and it just doesn't work. You will need to be able to determine if it is because their boots dont fit, they are not initiating it correctly, or any number of other reasons. Accurately being able to diagnosis skiing ailments is the peice of the puzzle you won't have, that a certified ski instructor likely will. The good ones will be able to spot something in mere seconds that it will take you hours to figure out.
In my opinion, the DTP system Harb and Lito recommend requires more out of the first time skier and the first time instructor, immensely so if the student is not naturally athletic or fearful. Terrain selection (the flatest, widest green run you can possibly find) is absolutely essential to your success. If you don't have access to that, you are in for a long hard road.
So, as you can see, it is much easier to by pass all of these hurdles and find a qualified instructor to teach them these things. That said, after having gone through a lot of the pain of the aforementioned scenario, and getting her a lesson with an instructor for her first time out, she progressed to linking turns on easy green runs for the first time with my help. In the process we got her custom fitted for boots, and the breakthrough finally occured on ski blades so it took a lot of patience, trial, and dedication on her part. I would have much rather gotten her more lessons, but her work schedule prevented that, so we did the best we could and found success.
So in summary, yes it can be done, is much much harder than you think (if you want to do it right), and is probably more rewarding to participate in the process with an instructor rather than try to do it yourself.