Hmm where you have a conscience we have something I like to call the void or if you have seen the movie "Never ending story" you could think of it as the nothing. The nothing is an emptiness inside us that usually contains our pains and suffering. It compells us to take action. If we don't obey it we become restless and unsatisfied. The nothing only requires one thing.. stimulation.
This is where a lot of sociopaths go bad. Stimulation for us is more difficult than it is for you. Usually we have to do something of risk to get that alive feeling. So dangerous driving, offroading or something to that effect. However, you can gain stimulation from toting with others but it leads to further negativities.
So maybe when your husband watches these sad movies it reminds him of his pain from the void inside him. Also think of yourself as his possesion. The more value you can obtain in his eyes the more he will pay attention to you. Not sure about the kids. I'm real close to my daughter but then again I raised her and she is like me. Hmm.. well my mother is a sociopath and she loves me more than my brother because we are the same. So I would say those kids are not like him and therefore they are like their mother instead. I'm sure he cares about them on some level but they aren't a part of him. Maybe he isn't associating them as an extension of himself.
Same with my brother. He is like his father while I am like our mother. (different fathers). So my mother and I have that strong connection and he just doesn't have that with her. She still loves him and does things for him but he just doesn't have that closeness. Your husbands lack of concern with the kids is still odd. Then again I never bothered going to the hospital when my brother was born and I care about him.