In reading the entire article, the reported snubs took place in 2011. Please note the letter Caroline wrote for in June of this year. Seems all is well. Lol
I suspect Caroline just wrote Obama off a while back. It may rankle but her anger must have cooled off by now.
She signed the letter supporting him, because ... well, support for a presidential candidate is an easy way to keep her name in the papers and the family's influence half-way alive.
If she didn't sign on with Obama and support him publicly we wouldn't be hearing about her and talking about her now.