The best way to describe the Walls family would be nomadic. Dad dislikes the idea of confinement so much that he'd rather just hit the roads indefinitely. Unfortunately, he's got a bunch of kids he has to tow along with him.
Later that night, Dad stopped the car out in the middle of the desert and slept under the stars. (2.3.19)
As a child, the lifestyle of living outside in the great outdoors is appealing to Jeannette. She romanticizes sleeping under the stars instead of thinking about it as a form of homelessness. Maybe she's not totally wrong, but the fact is that she doesn't even know what she's missing.
Some parents worried that their kids might get hit by lightning, but Mom and Dad never did, and they let us go out and play in the warm, driving water. We splashed and sang and danced. (2.4.16)
Jeannette is aware that her parents are different from other parents, but she seems to be grateful, at least at this age, for the freedom their lifestyle allows her—and for the good memories she has as a result.
"These cities will kill you." (2.7.14)
Dad has a distaste for cities because he sees all the buildings as great big concrete cages. He sees himself, on the other hand, as an animal living in the wilderness.
Rich city folks, he'd say, lived in fancy apartments, but their air was so polluted they couldn't even see the stars. We'd have to be out of our minds to want to trade places with any of them. (2.9.5)
Maybe if Dad loves the wilderness so much, he should get a job as a park ranger. But getting a job is something that's also too confining for Dad. He wants to be so free that he won't even have to live in reality. That's hard to do even under the best circumstances, but it's even harder when you've got a bunch of kids to take care of.
"No one else owns [the stars]. You just have to claim it before anyone else does." (2.9.8)
With Dad wanting to be free himself, it's ironic that he thinks he can lay claim and own something as ephemeral as a star.
"He's a good animal. […] Not happy about being in this damn cage, but he's resigned to it, and he's no longer angry. Let's see if he's hungry." (2.24.16)
Dad is talking about a cheetah here, but he's also talking about himself. At this point, he has resigned himself to having a job and being "caged" by the Man. Eventually, he thinks he'll break out. But we should note that unlike a wild animal, Dad isn't able to actually care for himself in the wild.
"I'm not upset because I'll miss you," Mom said. "I'm upset because you get to go to New York and I'm stuck here. It's not fair." (3.26.23)
Mom doesn't realize that she is only "stuck" because she chooses to stay with Dad. She would have a little more freedom if she would try to make it on her own.
"I think that maybe sometimes people get the lives they want." (4.3.18)
Jeannette starts an argument with her college professor, saying that homeless people maybe want to be that way. From her personal experience, that's kind of true: her parents chose to be "free" instead of finding jobs. And homeless is where it got them.
"Your father and I are pioneers," Mom said. (4.8.2)
Mom always maintains her positive-slash-delusional attitude, seeing herself as a champion of freedom. What exactly she and Pops are pioneering is a bit of a mystery, of course, but oh, well.