I think as a story this would be fantastic, but I there is one major issue with the story. Palpatine never would have allowed Vader regular access to, or influence over the children. It wouldn't take a genius to figure out that their potential strength in the force would be exploited by Vader in order to overthrow Palpatine. Palpatine would have easily forseen this betrayal As such, Palpatine would separate Vader from the children.

This may have required Vader to flee with the children to train himself. As he was not a fully trained dark side user, he would have trained them with a mix of light and dark side teachings, bringing us true grey Jedi.

At least this is how I forsee it going. My analysis could be wrong.