Oh, mutt! omg I'm so sorry! I remember too well the emotional hades caused by Katie doing a similar stunt.
Could difficult child ask the police if it would be ok to post Missing photos up on facebook with yours or his phone numbers as contact numbers should someone spot them? I've done this for endless people over the past couple of years, and not all of them are amber alert status. But shoot, I have a zillion fb friends all over the country (not to mention the world) and there are a LOT of us here with fb accts who can also post. It would spread like wildfire and you'd stand a good chance of someone spotting them and giving you guys a tip on their location. (if for nothing else, then to have a location for the custody suit)
Just a thought. Might cause them to run, probably not as they're no likely checking into fb right now.
Saying heavy duty prayers for you, difficult child, and them. Please keep us updated.
(((((hugs))))))