Rex Walls resembles a terrible sitcom dad, like Homer Simpson or Peter Griffin, except he's not a cartoon. The problems Rex causes have real consequences that aren't solved in 30 minutes.
Jeannette's dad thinks of himself as a wild animal. He's strong. He's untamed. He's got keen survival instincts. This is all true. But Dad doesn't realize he has the weaknesses of a wild animals, too. He's shortsighted. He's driven by fear. And he's totally lacks responsibility. When was the last time you heard of a wolf holding down a job and supporting his family? As cute as a wolf might look in a tie, it just doesn't happen.
When Dad says, "You can't kill something just because it's wild" (2.24.3), he's talking about himself just as much as he's speaking of the mountain lion that was shot. Dad also identifies with a cheetah in a zoo that is caged up. Dad considers himself caged by a society that expects him to get a job and support his family. Dad reacts exactly how the cheetah would, if given the chance: he runs away.
What Dad is best at in life is skedaddling (2.4.1). Whenever there is danger, he runs. Sometimes he drags his family with him, and sometimes he doesn't. He justifies his running with paranoid delusions, saying that the FBI or the Mafia is after him. Mom humors him, but she says to Jeannette, "It was more fun having the FBI on your tail than bill collectors" (2.4.2).
Jeannette describes her father as "a dramatic storyteller" (2.4.29). That must be where Jeannette gets her skills from. But instead of writing a book, or doing anything productive with his talent, Dad turns his real life into a fantasy, one in which he is a hero saving the day. In reality, he is the villain ruining every day.
Dad tells Jeannette, "Never play the slots. […] They're for suckers who rely on luck" (2.13.5). This is classic Dad, implying that he has a skill at gambling when he really has a gambling problem. He also repeatedly says things like, "Don't I always take care of you?" (2.3.5), as if his family saying yes means it's true, when it couldn't be further from the truth.
Dad has severe insecurity issues. His ego problem is apparent on the memorable Christmas Eve when he lights the tree on fire. Dad, it's supposed to be chestnuts roasting on an open fire, not the tree itself roasting. Dad is upset that the family has presents he didn't buy them. And like a true selfish egomaniac, if Dad can't provide the family with presents, he doesn't want anybody else to have any.
We've said a lot of bad things about Dad, and we haven't even talked about the fact that he's a cheater, he has a drinking problem, and he practically forces his daughter into prostitution. The family lets him get off easy. Mom even calls his alcoholism a "drinking situation" (2.4.22).
Ultimately, it seems that Jeannette does forgive the old guy. She's never too harsh on him, despite all the terrible things he does. He is her father, after all. When he rescues Jeannette from a burning shed, Jeannette shows us that Dad actually does care when his children are in legit danger. He's just blind to the fact that he's the one putting them in danger most of the time.
And the final story about Dad that Jeannette shares is all about how he somehow came up with almost $1,000 to pay her college tuition. We know, it's shocking that $1,000 could pay college tuition, but this was a long time ago, when the Boomers had it good. But anyway, the point is that Dad actually does something unselfish for a change. Jeannette leaves us with this positive image of her father because it's the positive image he wanted to leave her with—you know, before he skedaddled into the afterlife.