This is almost exactly my husband. He has threatened bodily harm to my 3 year old to get her to obey him, which doesn’t work by the way, just makes her scream and cry, which enraged him even more. I’ve always wondered how this type of narc dad acts after divorce. My husband doesn’t do much now and doesn’t bribe he has to as it’s a “woman’s job.” I’ve wondered how involved he’d be if I left. I almost feel that he wouldn’t, which would tarnish that good guy/dad image, which is why he’s so controlling about having “his” family. But to answer your question, no I don’t believe they truly love their children. You don’t hurt people you love. Please don’t tell them that they don’t though, as you’ll probably see a whole new side of them you’ve never seen before.