I'm sure if she really didn't want pictures of them out there, she could do something about it. After all, Jeff Brazier managed to get a watertight legal contract which meant the press or paps couldn't publish pictures of his sons after Jade died.
Unfortunately for the Price - Andre kids, her vow to stop showing them in public appears to be more about point scoring than their actual welfare
Jeff Brazier had to remove them completely from public eye, and with Lampard the kids weren't really in the public eye much so were private individuals.
But while one parent is basically making a TV show around them there's no argument that their privacy is being invaded.
People are very quick to say that Kate's just saying it out of spite but the one sentence above is why nothing can be done - aside possibly her going to social services and saying he's using them for profit but then if they get paid personally to appear (which i would think they do) not sure if she could get that past the post.