Rex and Rosemary Walls are not "traditional" parents. Rex is a nomadic dreamer who is always one step ahead of the bill collectors and drags his family from place to place through the desert and then across the U.S. to West Virginia. Rosemary is a certified teacher who chooses not to work so that she can be free to paint instead.
The children (there are four of them) are impacted by their parents' behaviors in a variety of ways, but the total lack of structure, money, and stability influences how the kids mold their personalities. One example of the deep love Rex has for his children is when he lets them choose a star from the sky to claim as their own as a Christmas present. He teaches them about astronomy and mathematics and science, letting them experiment with the world in order to understand things better. Unfortunately, his inability to keep a job drives him to drink, which scares the kids. At one point in the book Rex tries to run over his wife in the middle of the desert - while the kids are in the back seat screaming. Not exactly a great role model. Later in the book, he gets raging drunk at Christmas and lights their tree on fire, ruining all the presents underneath it.
Rosemary is a bit different. She doesn't seem to love her kids as much as she loves herself. She refuses to get a job, hoards what little food they do have for herself, makes the kids leave behind all their belongings when the family has to move but insists on taking her art supplies, lets her in-laws physically and sexually abuse her children, and (perhaps worst of all) doesn't disclose to anyone that she has a million dollars worth of property bequeathed to her by her mother. Money was available the entire time the children were starving, but Rosemary was too selfish to cash it in.
The kids become convinced that they will never live the same way as their parents. They become incredibly independent - even moving to New York City - alone - while still in high school just to escape from the terrible conditions in West Virginia. The biggest casualty is probably the youngest child, who ends up a drug addict who stabs her mother in an altercation, gets put in a mental ward, and then runs away to California. All of the children were abused in some way, but for the most part it convinced them that they could be in control of their own circumstances and be happily independent.