I'm sorry the two of them are stirring up trouble. Good for you for having the sense and serenity not to reply to the Rat's email.
About leaving the country...I don't know how the law applies after D, but while we were separated, XH and I had to get a notarized form from each other each time we took S14 out of the country.
I doubt seriously that your XH and the Rat could take your children out of the country without your permission. But this is definitely a question for a legal expert, i.e., your L!
My best friend always says, jokingly, "no good deed goes unpunished!" I know it looks right now like your stretch of good behavior is being punished, but you know it isn't. Just hang in there.