I have a grown cat (Vivi) who has never liked to be picked up and cuddled, even from a kitten. Sasha is just the opposite - loves to be cuddled. I guess individual cats can just be different, just like dogs, or humans for that matter.

I think you're doing the right thing for the biting kitty. I know it's frustrating too, and yes, the pictures of sweetness and love (although I love them) make me wish I had that, because Vivi and Sasha romp and play fight ALL THE TIME - I've never seen them be affectionate toward each other. Such is the life of a cat lover! It'll get better - promise.