There is a section in the LDW FAQ section that addresses how to properly backup your savegame files and have them switch over to another computer:
Can I back up my savegame files and/or move them to another computer?

There is also a section for installing the game on another computer:
How do I reinstall Virtual Families for Windows or install it on a different computer that I own?

Make sure you put in your savegame files after installing the game onto your other computer just to avoid it getting overwritten with a blank one.