He's put his divorce on hold for three years, in order to aid in the investigation. He's actually done the opposite of what you've written. He's put the investigation into his son's disappearance before his divorce. I can't think of many people who would want to remain married to someone they believe to be a murderer. He's made huge sacrifices for the investigation.
I guess I really don't understand the Kaine suspicion.
He was at work when Kyron went missing, and this was verified.
Were I Kaine, I would have asked my coworkers not to speak to the press as well. To me this is only logical in the early stages of an investigation. They should be speaking to the police, not reporters.
He cooperated with LE, he aided the investigation and he was available for LE and questioning nonstop.
When LE told him he and his daughter were in danger, he moved her to safety and protected her through legal channels. Far from focusing on his divorce, he allowed his divorce to be put on hold to help the investigation of his missing son. He put his missing son first.
As far as I can tell, he hasn't done anything suspicious at all.