You can save a house in the library and then plop it down on a bigger lot. Save your current home to the library, go to the larger lot you want, go to the gallery/library section and grab your house and then Replace Current Lot.
The old house is there, centered. You can use the move tool to move it around and find a better orientation for it in the new lot if you need to.
I have not done this with an occupied lot, just an empty house moving to a larger space. I don't know if it works with a family.
The move function in the computer is for the household to move to a larger better home. You can keep your belongings or leave them as you did in Sims3. You have the option of moving to any neighborhood or even move towns (this will be very cool with expansion towns!)