Having to move each family member in one by one this way is tedious but they will probably bring some money with them, whether they'll bring all the money they had previously, I don't know. I've never actually done this so let me know if it is not the case.
To move them all out except the Sim you want to play, have one of them "move" with a phone or computer. Then select the Sims you want to move out but keep your active family as the one with the Sim you want to play (should be selected for you.) Now you can either "kick out" these Sims, which moves them into a random house large enough for them, or you can select a lot or house for them to move into. If you chose the second option, either a house or a lot, the money to buy the lot or house comes out of the family funds. Your Sim is essentially buying the house for them.
When you click the final check mark, the Sim staying in your active household will be free to do as you please, nothing will change there. The family members moving out will now be removed from the interface on the left (where the household head shots are), the Sims will gather on the curb and a cab will take them to their new home. Anything in their personal inventories goes with them.
The Sims 2 didn't have story progression the way the Sim 3 does. You can turn it off under (...)/Options but then all story progression elements will be turned off: no births, birthdays, deaths, moves, etc.