Originally Posted by NoMoreJuice!:
I have this little guy, except mine is 20 months. He's a tyrant, demands cookies or he won't get in the car, has giant soul-shaking screaming fits when he doesn't get his way (which is all the time here and never at home, haha). I've had him for 2 months now, and he's SO MUCH better than when he started. Everything Blackcat suggested is right. Screaming at lunch=straight to bed with no second chances. Saying "Go Play" and walking away from him consistently will force him to be independent, and he will definitely walk when he finds it necessary. The parents will stare at you blankly if you try to get them to change their habits, or they'll lie to your face and tell you they will, but absolutely nothing will change at home. The only chance for peace you have is to get very tough and be very consistent. I can't actually stress the consistency enough, it is the key.
It DOES get much better eventually. Good luck!! 
I too have this dc child, she is also 20m. The first few weeks I was unsure I would keep her (she started right at 12m). By doing pretty much what BC said has worked miracles. She is a fun and easy going kiddo now. Well with a few quirks that I swear dcm taught/conditioned into her!
Talking with DCMom got me no where! Dcg was a bear the first week after Christmas break (was out for nearly 2 weeks), then all good again.
I believe most can adapt to behaving differently at day care and home. It just takes consistency. Good luck!