Alexander was farmed out to his mother, who was Half-Klingon and thought most of the ways of the Klingon were lame and stupid (which they are)
Worf shps him off to his step-paremts who are old and cannot handle the child. Worf more or less ships the kid back to the grandparents. He's too busy guarding Picard's back.
The kid grows into a man and wants to fight in the war against the Dominion. He's 3/4th Klingon. Yeah, he's a fuck up, but according to Martok "He's a good boy, with a warrior heart (the ultimate compliment from a Klingon) and he tries hard." He fks up, oh well. He might be the Reginald Barkley of the Klingon Empire. Reg was honorable. Slightly.