Again, I am not so much as angered or annoyed by Palin's actual photos as I am by the absurdity of your arguments, excuses, and what if's. You're full of excuses. It doesn't matter if it's Palin or anybody else who is a public figure. If you post something in a public forum and your posts have been discussed on the national news, then you should expect people to talk about your photo including how you handled the situation beyond that photo.
I don't expect her publicly chastise her children. That's ridiculous and would only serve to humiliate and embarrass the child.
Instead, I am saying if Palin thought it was wrong he stood on the dog (as you suggest) and admonished him private (as you suggest), then she could simply express her opinion publicly such as, "I wasn't happy to see Trig standing on the family dog, but as a mom, I thought it was cute and had to take a picture and shared it." And that would end the entire controversy.
That would be reasonable. That would be acceptable IMO. I don't think think she needs to do or say anything beyond that. She doesn't need make a huge ass apology on FB, donate money to an animal shelter, or chastise Trig publicly.
But everything you suggest as a possibility doesn't seem to reflect her actual opinion on Trig standing on the dog, and we see that in her response and management of this issue on her FB page. And again, I don't care so much that Palin isn't managing this very well. It's expected of her IMO. What I find more irritating than the actual photos is your excuse upon excuse and never ending stream of hypotheticals and more excuses.
Sorry if that's offensive, but I am being honest.