We've all had difficult children in our daycares DisneyPrincess. We can't just let them run amok! Rules have to be followed or the inmates will take over the asylum and we'll be the ones who go insane. You have a right to be super angry, you are well rid of this parent and child if they are not on the same page with you for raising a well behaved child and I'm sure you will find a better family.
Now you know something you have to watch out for in your next interview and you've learned a lesson about something you will not tolerate in the future. I learned these lessons too and it certainly made me a better and more honest interviewer. Which helps weed out the families that are going to cause me grief before I even consider signing them on. Sometimes people will fool you but I wish you better luck with the next clients.
Shake it off as best you can and have a great weekend. It's for the best. Envision your days ahead WITHOUT this family and you should feel better.