One way to puzzle this out is to consider what claims TH could make against KH that would result in pending (under investigation, but no indictment formally filed) criminal charges. Here’s a list of potential criminal offenses:
http://criminal.findlaw.com/criminal-charges/view-all-criminal-charges.html
My guess is a claim of domestic violence, which is not unusual in rancorous divorce cases. Maybe possession of drugs or drug paraphernalia. Maybe criminal harassment:
“Generally, criminal harassment entails intentionally targeting someone else with behavior that is meant to alarm, annoy, torment or terrorize them. Not all petty annoyances constitute harassment. Instead, most state laws require that the behavior cause a credible threat to the person's safety or their family's safety. - See more at:
http://criminal.findlaw.com/criminal-charges/harassment.html#sthash.X5VCkObu.dpuf”
IMO, it’s doubtful the pending criminal charges have anything to do with Ky’s disappearance. It’s more likely a “counter charge” brought as leverage for TH in the upcoming custody battle.