Actually, a lot of lawyers will take cases like these just for the publicity (and 20% if they win). If the next hospital finds the same as the second opinion they got, then the first hospital is not only guilty of being asshats, they are guilty of malpractice. If the story is true, they were trying to force the parents into choosing an unnecessary open heart surgery for their child and prevent them from getting a second opinion. Suing the state may or may not be a viable option, but suing the hospital seems like a potential winner to me.
Yes there's a big difference between suing a private entity and suing the state, but should there be?