Options on the fate of the family...
So this is what I think are some of the possible options.
1. There dead Jim!
The easy one, they died during the blast or its aftermath and you'll find your spouse's bones outside the Vault. (they will be they one with the wedding ring).....like the one you have in your inventory.
2. Frozen with you but removed earlier.
This is more complex and could tie in with option 3, basically they were brought into the vault with you and they were revived and left earlier than you, you are then revived and find yourself the sole living thing in Vault 111.....get out there and track down your spouse and kid.
3. Android family.
Your family were put on ice, but didn't survive the process. the preserved corpses of Vault 111 was used by the Institute for their experiments and if you co-operate with them, they will program an android with your spouse's memories from their preserved brain....and they will throw in a android kid for free.
4. Evacuated by the military.
We know that the military were on site when the blast wave hit, but there is no sign of any wreckage of the vertibird or apc from the prologue when you emerge, so perhaps your injured spouse and baby was evacuated with the soldiers guarding Vault 111, find out what happened to them next.
5. Ghoulified.
They became ghouls, this is a strong possibilty since unless your spouse got into a vault or bunker they probably would have followed the usual Fallout game rule of nukes = ghouls. The baby would present a problem since there has never been a baby ghoul in any Fallout games (not including games that were never made).