An English person with two children of 15 and sixteen could get a job in Scotland next year. He would then be in time to be put on the voter's role; as would his now 16 and 17 year old children. They, knowing that they won't be in the country in a couple of years because their dad is going to move on, couldn't care how or why they vote.
By the same token, a Scottish person with two children of 15 and sixteen could get a job in England next year. Assuming he is not a service voter, if they change their permanent residence none of them will be able to vote in the Scottish referendum. That sort of thing is inevitable.
Going back to your first family, if they couldn't care how or why they vote, I suspect they won't vote.