I will still say that your lawyer telling you to call her after all the work you've done to set-up email communication was a bad idea. Your ex is not normal...she lives for strife and confusion around her. And nothing about what has happened recently is surprising. Quite the opposite, it was extremely predictable.
She's one of those women that go from crisis to crisis and will look for a soft place to fall or some temporary white knight to bail her out of whatever problem she thinks she's in at the moment. She was hoping that you'd tell her she could come live with you. I hope you realize that. You've done a good job of being clear that you're available for the kids but not available to solve any of her personal life problems.
You did the right thing by simply telling her you'd keep the kids, thanking her and hanging up but you might want to start easing your way back to 100% email communication and not get drawn in to being the confidante for her crap life by phone...its a bad idea long-term.
I wouldn't get involved in anything else...even to do with the kid's belongings. She will have to sort that out with the ex-bf.
^^^^^^^^^ this post is BANG ON !!!!!