The show used the term "family annihilator" which is, apparently, actually a thing. The LaCroix character also said that the husband was a control freak.
"Categorizing the Killers: Four Types of Family Annihilator
Self-righteous: The killer seeks to locate blame for his crimes upon the mother who he holds responsible for the breakdown of the family. This may involve the killer phoning his partner before the murder to explain what he is about to do. For these men, their breadwinner status is central to their idea of the ideal family.
Disappointed: This killer believes his family has let him down or has acted in ways to undermine or destroy his vision of ideal family life. An example may be disappointment that children are not following the traditional religious or cultural customs of the father.
Anomic: In these cases the family has become firmly linked in the mind of the killer to the economy. The father sees family as the result of his economic success, allowing him to display his achievements. However, if the father becomes an economic failure, he sees the family as no longer serving this function.
Paranoid: Those who perceive an external threat to the family. This is often social services or the legal system, which the father fears will side against him and take away the children. Here the murder is motivated by a twisted desire to protect the family."