brit, the antitime Enterprise form yesterdays Enterprise and the regular Enterprise were exactly the same size even though one was built as a troop carrier in a time or war and the other was built in peace time.
Taking "familes" with them was joke by architects who wanted to build shps that could be quickly retrofitted into troop carriers for when peace tiime eventually transitioned into wartime.
A state room for the wife and 2 kids can easier be turned into a billet for 12 Starfleet marines in a couplke hours by the engineering corps.