Re: Is there a way to undo changes made by "neighborhood stories?"

No, not really.

If the issue is only unwanted kids/pets, you can just delete this completely from your game. If the NS killed sims, then there gone forever. 

The reset toggle is just to ... reset the settings (Turn all settings on again). If you don’t really want a NS-progress you should uncheck it under options, but this is of course not retroactive. You stuck with the changes which NS gave you before you toggle it off. I toggle it complete off as it was release, so I never had this issue that I can’t toggle it off.

Here is a bug report maybe you should me too if these toggles don’t work for you.