Crucifixion is a curious topic -- for all its subsequent religious significance, there's surprisingly little information about it. The Romans simply didn't speak of it much, and I'm not aware of any reference to "crucifying entire families". Indeed, I'm not aware of any reference to the crucifixion of women or children at all.

We do find reference to mass crucifixions, for example Plutarch tells us that that was the fate of some 6,000 of Spartacus' army. Appian has an anecdote that Spartacus had, for his part, crucified a Roman prisoner -- this would have been particularly galling to the Romans, as this was an ignoble death for a citizen. For the Romans, touching the Earth was part of a certain dignity of the spirit-- being raised above the Earth at death is a kind of defilement.

We find crucifixions mentioned in Josephus and in the Lex Puteolana as well as a few other fragmentary sources, such as a grafitto from Pompeii. It's plainly a punitive mode of execution, intended to humble a subdued population, to punish slaves, and perhaps to entertain an audience at gladiatorial contests.

Beyond that, we know very little. We're not even completely sure how it worked, mechanically. Its represented as vindictive and intentionally humiliating and cruel, and the circumstances in which its mentioned suggest that the cruciarii are men who have themselves done wrong in some dramatic way, rather than their relatives. Romans were generally eager to take slaves, who were of economic value; we don't have the kinds of family punishments that you see in, say the Ming Dynasty's celebrated "Nine Exterminations".

You might also think a bit about how Romans thought about "families" -- not the same way we do. This was a male dominated culture, and if they'd killed the adult male, and sold the women and children off into slavery "the family" no longer existed.

See:

Cook, John Granger. “Crucifixion as Spectacle in Roman Campania.” Novum Testamentum, vol. 54, no. 1, 2012, pp. 68–100.