They never fought at all. There was zero conflict. It wasn't that they just "hid it from the kids"—there was simply nothing to fight about. They were truly each other's very best friend, and intensely so. My dad tried dating again a few years after her death, but I think he soon realized there was no way anyone could capture the kind of companionship he had with my mom. Some people are able to love more than one partner over the course of their life; I think he decided he could not.
He's a very private person, but I know he constantly thinks about her every day, and I suspect he's pushing off retirement because he doesn't want to be at home without her. They would have just hit their 40th anniversary if she were still alive.