Welcome to our Forum, Dragongirl!
You don't have to turn off aging or story progression in order to move out a Sim. Just have your Sim use the computer or cell phone and select "Move" to get the process started. You'll have the option of buying a house or just kicking them out. Either way gets them out of your house and out from under your control.
Whether you play with aging on or off, it will control the aging of every Sim in town, not just yours.
I hope you find this helpful.