Good point about their "middle class" sensibilities, that does seem odd, given how they were living. It might be more interesting and plausible if the kids were more cynical and feral, or possibly more loyal to their parents, living in a society where safety and resources were not assured.
And since the Dad is a cop, did he ever kick down doors of people with three kids to enforce the draconian laws? That might have been another way to make him more interesting, if he realized he was living in a society where he was forced to be a hypocrite, and wanted to find a way out, even if it meant having to fight dinos.
In fact, forget the third daughter. Maybe the way to handle the backstory is that the family is living in a protected part of the city, with spacious quarters and domed parks, because they're part of the elite. Daddy is a cop who kicks down doors of the less fortunate in support of a corrupt system that protects the elite from the environmental degradation around them. Mommy is a doctor and also part of the elite. The kids are spoiled, nasty little brats with an unearned sense of entitlement, just like all their friends in Dome City.
Daddy finds out about the Terra Nova project, which people in his own social class don't care about, since they're not going to leave their cushy lives to live in a dinosaur infested jungle. But Daddy realizes the family must leave, because dinos are better than their soulless existence. He's different from everyone else - he hasn't been utterly corrupted.
That makes the parents look more heroic because they didn't really need to leave. It gives us some interest in seeing if the kids can be smacked out of their bratty ways by their new, difficult lives. Dad is overjoyed to be seemingly living in a "clean" society where everyone is equal and pulls together for the common good. And then the suspicions start to mount...