Since I haven't read the exact novel, I can't be sure. But likely, the father is one of the main characters. There might also be the mother and the children in the family.
Without having read 'life with father novel', it's hard to say precisely. However, it's reasonable to expect that the father is a central character. There may be a mother figure, and depending on the nature of the story, perhaps the children are main characters too. It could also include other relatives like grandparents who might influence the family dynamic. Additionally, there could be characters from the father's work or social circle that come into play in the story of life in the family with the father.
I'm not entirely certain, but I would assume that the father is a key character. There could also be other family members such as his wife, sons, and daughters. Maybe there are also neighbors or friends who interact with the family and play important roles in the story related to life with the father.