I'm just doodler and I don't really know anything, but if you want her out, I suspect you could boot her out (assuming there are no laws against that). All the constraints regarding her image and children are her constraints, not yours, but you're using that as an excuse to not do anything.
You can always tell her that the children can split their time between the two of you as soon as she finds an acceptable place to live (someplace you approve of).
It's not fun or easy, but I think it's your choice (again, assuming you're not breaking any laws).
