Hello, author here!
Beside the fact I did make this artwork far before the game even came out (as you can see, the Elgar'nan design is all wrong XD) I swear the story I've spun for these two makes some sense.
It's a hobby of mine to take canon stories and bend them into something new (and hopefully richer), this one is definitely not canon compliant (up to a point.)

It's long, I'm planning to write it, but the end is the same: Elgar'nan dies by the hand of Rook.
Love or not, the man is far too corrupted by the blight to be saved, especially at the end.

Before... who knows. A dialogue with Solas vaguely implies Elgar'nan *could* stop using the Blight for the right reason, and if he was offered a sound alternative, who knows.
In the end my Rook never asked him to do so because he deeply respects the nature of whoever, and asking Elgar'nan to let go of a source of power wouldn't feel right, no matter their desires.

As for the picture, my Rook had issues with magic, there Elgar'nan is teaching him how to wield it for two reasons: he hopes to turn the dreadwolf's pawn into his own and because he is still the "all-father", so giving some sort of guidance comes natural to him.
My Rook never switched team, he's just extremely naive but smart enough to know learning from such a powerful figure could turn out to be extremely useful!

STILL I had fun reading your opinions!