It's been a while since I've done this, so sorry if I've got any instructions wrong, but go into Edit Town and then click on the icon of the house your family currently live in, then a square will come up with a picture of the family and at the bottom there is an icon that says "Save household to library"? Click that and it'll ask you if you want to save the household or the household
with the house. That's what you want, so click that. Then, once you've downloaded UC, load up your brand new save file and at the stage where you choose what sims to play, you can choose your family from the other town who should be waiting there in the clipboard.
Note that they will all keep skills, etc. and relations with each other but they will lose absolutely all relationships with the other sims in the previous town. Hope this helps.
