Yes, you can. You can change between them in 'Edit Town'. Just remember; with the option 'story progression' the family you are not controlling may move, divorce, have a child etc. So if you wish to keep them intact you might want to turn that off. Also, with the option 'aging' that other family will age while you are controlling the first, so this you might also want to turn off.
However, these options influence the whole neighbourhood, so with these options off, no family will age (including the one you are for the time controlling!), no new families will move in and no families will have a child on their own. All that you have to force them to do. You can still age your famliy members with the birthday cake, but normal townies will not age.