Question: A friend alerted me she saw my children in a photograph hung in a chain restaurant. Although the picture was taken at a public event, I never gave permission for anyone to sell the image of my children or to hang in such a very public place. Even though it is a public place, there is some expected right to privacy. After all, we don't expect a trip to the grocery store to land us on a billboard. What rights do I have to protect the image of my children? (What if we had been in Witness Protection or hiding from an abusive partner?)

Answer: 
My answer will be really short, and not based on any law school experience, but only on some conversations about privacy and tort law, etc. and how they apply to photographers, with an uncle who is a lawyer and a cousin in law school, and the fact that I'm a photographer.

As long as the person who took the photo in the public place isn't deriving any profit from the photograph itself by sole virtue of your presence in the photo, or committing libel against you, then your privacy isn't being exploited for others' gain and harm isn't being done to you. So in that case, there would be nothing you could do to them.

Harm can include intangible harm like suffering caused by knowing that an indecent photograph of someone you love is being looked at by others.

"By sole virtue of your presence" means the person alone who is the subject of the photo, rather than the context of the photograph. I.e., I can be paid by the newspaper for my picture of the the winner of the state track meet, and of course that photo consists almost entirely of the person who won. But there is an editorial reason for the picture, i.e., it is a picture "of the winner of the state track meet" rather than "a picture of a person that some other person is hiring me to stalk in public." 

Being a celebrity is enough context that people can usually "stalk" celebrities in public legally, but most other people can't be stalked in public without its being construed as harassment.

Sorry, my answer is now getting longer and longer... just look at the second paragraph, and that's all I meant to say.
Photographer here. This isn't a question about privacy, but rather commercial use of your image by a private company on private property which is open to the public. You and your kids have the same rights that a child actor from Modern Family would have. The restaurant hung the picture to enhance their commercial interest. You can't do that without written permission and pay.