Hi, Brett. When your parents listen in the family room, do they turn the speakers off in the living room?
If they don't turn them off, and if you can't find a receiver with A/B switching that you like, you could also consider using the "All Channel Stereo" (or equivalent) feature on a receiver that doesn't have A/B outputs. Your parents would normally run the system in stereo mode to use the two speakers in the living room, but they would turn on that surround sound mode to then play the same signal through both sets of speakers.
If they do turn them off, you could also consider getting a speaker selector box. Those have buttons on the front to choose the set of speakers that they want. The less expensive ones are manual, so they'd have to push the buttons (no remote control), but they cost about $20-$40.