Their emergency petition was 6-12-12.
Yes, but if you look at the timeline, in 2011, they were in the news media because of their son, Jacob. No mention of their adopted daughter. I suspect the newfound attention they were getting is what made them regret adopting a child with special needs and they needed to figure out a way to get out of it without it affecting their public persona. I think that's when they were tucking her away in mental institutions while they traveled around giving interviews. I can't find a single photo of N from 2011 and only 1 photo in 2012 after they changed her age. I think they exhausted the mental institution route and had to come up with another way to ditch her without getting into trouble themselves so they changed her age, dumped her in an apartment and moved to Canada a few weeks later. It's possible N's care givers in those institutions finally caught on and realized the Barnett's were nuts and threatened to get CPS involved. In Kristine's head, that would be the end of everything for her. She thrives on the publicity her smart kid was getting her. So they came up with the age change idea. Below is just a sample of the things I was able to find.
2011
⦁ March 26, 2011 - 12 year old Jacob Barnett is featured in Time Magazine
12-Year-Old Genius Expands Einstein’s Theory of Relativity, Thinks He Can Prove It Wrong | TIME.com
⦁ March 30, 2011 - 12 year old Jacob Barnett is featured on Ripley's Believe It Or Not
This 12 Year Old Is Probably Way Smarter Than You - Ripley's Believe It or Not!
⦁ March 30, 2011 - Jacob Barnett is featured in a ParentDish article
http://www.tedmontgomery.com/remarks/11.1-6/Asperger/JacobBarnett.html
⦁ April 2011 - Kristine Barnett's website for Jacob's Place is created.
http://myjacobsplace.com myjacobsplace.com
⦁ April 6, 2011 - Jacob Barnett sets a world record for being the youngest astrophysics researcher.
Youngest astrophysics researcher: Jacob Barnett sets world record (Video)
⦁ April 11, 2011 - Jacob Barnett is featured in Discover Magazine
A (very) smart kid and a solid theory
⦁ May 2011 - Kristine Barnett and her 3 sons go to the U.K. and Venice. Where is Natalia?
⦁ August 5, 2011 - Jacob Barnett, the oldest son of the Barnetts', publishes his research paper in a physics journal.
Origin of maximal symmetry breaking in even PT-symmetric lattices The family receives public attention for their child prodigy son.
Phys. Rev. A 84, 024103 (2011) - Origin of maximal symmetry breaking in even $\mathcal{PT}$-symmetric lattices
⦁ August 14, 2011 - Kristine and Jacob Barnett appear on the Glenn Beck show.
⦁ October 2011 - Kristine and her 3 sons go to the pumpkin patch. Where is Natalia?
Jacob Barnett
⦁ December 15, 2011 - Warner Bros. buys the rights to Kristine Barnett's memoir
Warners buys rights to autism memoir