I solved my own problem be reading the command line options in the manual:
I went to ~/.config/darktable/library.db, duplicated this file renamed it personal.db, then ran darktable --library ~/.config/darktable/personal.db
. Then, I removed all film rolls except ones containing family photos. Then I started darktable normally, and removed the family photos.
Then, I added a function to my .bashrc file (I'm on Linux) and named it dt (for darktable). This function contains my line above, specifying the alternate library.
This is great because all my other settings are intact, and the same no matter how I start the program. I'll have to create another function, and another db file, for my work library.