Accept the commission.
For one, to be given a ship like this with its advancements in technology, suggests a high level of trust from Starfleet that it will be used responsibly. It’s the luxury of the Ent-D with a bit more advancements than the Ent-E without the same level of pressure that comes with being the flagship.
And second, the families on board are not a big deal. They have a right to explore too, and the ship is generally a safe environment. Whatever danger they are exposed to over the multiyear mission, the families already signed up knowing the risks.
What do officers on ships not equipped for families do when they have a child? Do they just leave the ship when it pulls into the nearest Federation starbase? What if the ship is in a situation like Voyager where they can’t? Do they decide to become a generation ship? And how does having growing families on ships not equipped for that situation affect the command styles of the captains of those ships? At least the Vesta class is equipped for such a scenario and the captain is already mentally conditioned to accept the responsibility that comes with the assignment ahead of time.