I jumped into my current game to test this out and it seems to be working for me. You have 2-3 ways to move your household to a different town. You can move either by phone or computer. Both work similar to each other. Or use Edit Town.
By Phone or Computer:Phone: Real Estate > Move > To New Town
Computer: More > Move > To New Town
* If you have a pregnant Sim in the household, you may not be able to move towns.
* Make sure your household has the money to move.
Once you are at the Choose a House Menu. You can choose a house or lot to place your household in. Then you can play your household as normal.
By Edit Town Mode:1. Go into your game and go to Edit Town.
2. Select the household you want to move and click Save Copy to Library.
3. Go to the Main Menu.
4. Click New Game or load the save you want.
5. Once game is loaded, select household you want to move in and select a house or lot you want to move them into.
5a. Or if you have saved them with house, you will need to Select household and place where there is a blue empty lot box.
6. Click the Return to Game Setup button.
7. Click Choose Household - to play the household you just placed. At this point you should be able to play the household!!