All the stories I’ve read about this case fail to mention the likelyhood of a follow-up action, so I don’t know what rights the kids’ family have to sue for additional damages, but one technicality that should be cleared up from the linked article is that the dogs were not pit bulls, since it would be effectively illegal even to own them.
Yes, the kids can sue. Without knowing more about the facts, it’s not possible to speculate about their chances of winning, but the fact that a criminal conviction was obtained does tend to suggest that they would have a good chance of succeeding in a civil action.