Then don't file for a revision; sounds like he may one day soon, and you can just add it then if he fights you for more custody.
Really though? Does it NEED to be in the papers? I realize most people have it in their papers, but honestly, if you refuse to let your kids go because he won't give you the address/last name whatever of this person, what's he going to do? If he calls the cops, and they come to you, you say I'd be happy to let them go, but he's leaving them with a babysitter whom he won't provide their name, and he won't give me his address, so therefore they can go as soon as I get that info. The cops are going to turn to him and say give it to her. He's going to say no. The cops are going to say well, take it to court, and walk away.
Might you get smacked in court for not letting them go? Maybe. If he takes you. But you know what? It's going to be a verbal smack, and then they are going to tell him to stop being an ass and give you the info. I say just refuse, and see where it goes. Make sure you have it in writing that you have asked him, politely, for the info.BS(me) 46, kids DS 17, DD 14.
He is no longer my best friend. Repeat until it sticks.
WH says marriage is over: May 15, 2009.
EA#2 July 20, 2009. Legally sep: Aug 16, 2009. DIVORCED!!!! Signed Nov 23, final Dec 24, 2010, adultery listed.