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.

@jirachiband 

You can move your Sim to a new save. 

1. Go into CAS and save him to your library. 
2. If you have modified his house, go into build buy and save it to your library. You can skip this step if you don’t care.
3. Create a small room in the yard, put the contents of his inventory into it, and save it to your library. Ditto for household inventory, if it has stuff you care about.
4. Start a new save. 
5. Confirm Neighborhood Stories is off.
6. Place your Sim in the house you want him in, replacing it with the version in your library if you did that step.
7. Place the room somewhere on the property and take all his inventory out of it, then delete the room.

I’vr had to do this for a corrupted save file myself, so I can confirm it works! He’ll still have his job, his skills, etc. What he won’t have is relationships with people outside his household, so if that’s important, move them in with him first, I suppose, and move them back out again after.

You’ll also lose things like custom holidays and clubs.

 Good luck!

I think you could use Manage Sims to delete the unwanted pets and babies but I've never tried it. Good luck with whatever you decide to do.

That works for pets and adopted kids, but the game doesn't let you delete infants through Manage Households. You need to have a sim physically go to the lot with the infants on it and use a cheat to delete them.

Sometimes I got infants from expand the family question. I just moved all infants via household management to a townie and then delete the household. No need to aging up these infants or play this household. // Not all cheats are access bar in a vanilla game or for console, and I think this cheat is one of this. You need a mod for full access to all cheats as destroy objects etc.