"Isn't it called right to one's own image"
No such thing. Some professional photographers may ask models to sign a waiver but this is legal arse covering and nothing to do with a persons "image".
"You cannot publish pictures of other people without their consent."
If that photo was taken in a public place or in private property with the permission of the owner then you absolutely do not need permission.
As I've stated in another thread, there is no such thing as privacy in a public place. Absolutely categorically not - that's why its called "public".
Take a look in any news paper sports section - do you think the paper asked the thousands of people in shot in football stadiums for their permission?
When I shot my last wedding, did I ask the permission of every individual in every photograph before I published photos on my site?
Do Tesco ask for your permission for taking your "image" on their CCTV if you walk through their car park?
Stop talking out of your arse.
To repeat myself, OP you have no legal or moral obligation to remove that photo. If the parent of the child in question does not want her picture taken then she shouldn't let her out in public - let alone to a party.
You may as a courtesy remove the photo (though I certainly wouldn't and I'd be clear in telling her why) but you are doing nothing wrong in refusing to do so.
This idiotic "think of the children" hysteria about public photography pisses me off no end. Your children may end up on someone else's photo album - tough. It's part of living in a free country.