These photos are being deemed unacceptable after the fact. That's part of the issue. It was ok that they were taken and first published (apparently). So a major part of this issue is that someone continues to control a photograph based on their later decisions.

They are not alleging that the photos were taken against the parents' (or children's) will. It seems to imply that a person carries a perpetual license on their likeness.

Maybe that children are involved makes this case special (unclear here). Or maybe someone who liked a photo of themselves one day gets to demand it be taken down later. Imagine a couple dating put up a photo. They break up and a couple years later one is getting married and demands the other takes down that photo.