My highest interest is in every child being placed in the most caring and loving situation. I have no bias about H's options, as I have never known any of the people involved. That said:
I don't think it is at all clear that H's father actually had notice of the hearing. If you read his version, he says he was out of state travelling for his work, as a musician maybe?, and to pay for Hannah's support maybe? He states that they knew how to reach him and did not, and that they knew how to reach his parents and did not. According to him, Jack claimed that he HAD called TAW's parents and they didn't want anything to do with H, so TAW pulled out his phone on the spot and called his mom in Jack's presence, essentially calling Jack's bluff. Jack turned beet red and refused to talk further. He also says that H's mother told him she was fighting for custody herself and he believed her. This turned out to be a deliberate falsehood intended as a ruse to mislead him. (can we say Logan?) This is all paraphrased from the article in the Examiner.
I'm not verifying the truthfullness of ANYONE's story here, but it seems fair to consider both sides, especially as we are seeing beyond all doubt that TS and JS have no problem lying when it serves their purposes in stripping a child of his/her parents.