This is aimed a bit at Palin and a bit at Obama, although Palin seems to be the more egregious of the two.
Rule for candidates: don’t trot your kids out on stage at every turn, for photo ops and then complain if the press (or the public) wants to know all about them. I think if you continue to put the kiddies out there then they should become fair game for the media. Even Bush seemed to know to go easy on having his daughters out in the public eye when they were younger, lest they face vicious media scrutiny.
If Palin keeps trotting them out as campaign props to try and sway voters, then when they get in trouble - and almost every kid is going to get into some sort of trouble - it’s tough to justify request for privacy.
Note that this goes for Obama, although I’ve only once seen his daughters on the public stage, as an “impromptu” moment during the DNC.