I actually agree with Davy, I think he has a valid point. Talk directly to the kids. Tell the 9 year old she needs to fix her age or you will have the account deleted and any other account created for her. Tell the children you will be getting access to the accounts and you will be monitoring them. I teach my children all of the time consequences in our decisions -- good choices hopefullly equate to good things happening, bad choices will end up with bad results. Her having herself as 19 is a bad choice and she needs to be taught and explained the bad consequences that could happen as a result. Parenting doesn't stop when the children walk out the door to the other parent's house. You won't be able to stop Mom from allowing it.
I understand they are at Mom's, but Mom is right in some perspectives (and no I don't mean in allowing these accounts). Unless she is putting the children in harms way (and there would be a big debate about that with these accounts), you can't tell Mom the children can't do something at her house anymore then she can dictate to you what can be done with the children at your house. Albeit not the best decision, it is her's to make. Same with "(Staying up all night, watching R rated movies, and much more.)"....you can't dictate to her how to parent.
This is one of those pick your battles. You know about the accounts. Find out what you can, monitor them, monitor who the kids chat with, I am sure there is software you can install for tracking....