The O'Malleys aren't exactly the Cosbys. Conor's got an absent father, a grandmother he doesn't exactly get along with, and a mother with a terminal illness. It's a recipe for a lot of family drama, and sure enough, we get it in spades. We enter Conor's life at a time when his notion of family is changing really fast, and A Monster Calls is all about how our boy copes with that fact.
Conor's grandma's denial that she's aging is similar to his mom's denial that she's dying.
When Conor's dad says that his house is too small for Conor to come live with him, what he really means is that his life (or maybe his heart) is too small. He's only got room for one family, both literally and metaphorically.