We are sending wedding invitations to a couple with two children. Do we use "and family" on the outside envelope?
No. Wedding invitations are sent to the adult member of the household.
In your case, the outside envelope is addressed to the parents who receive the invitations on behalf of their children.
Their children's names (not "and family"), if you wish to invite them, are written on the inside envelope on a line beneath the names of their parents.