I wouldn't ask her if she found an apartment. I would get her TWO THINGS :

1. A newspaper with the rentals section in it opened up for her
2. A family therapist business card tucked into a book on marriage and commitment... Or some other suitable book

THAT reinforces both those points above.

Don't talk to her, just act. You should collect a lot of articles that explain how destructive divorce is to children... with an eye catching title.. print them up and leave them on your desk...

She may read the book, she may not... articles are often more inviting since they don't look nearly as intimidating...

Maybe even print up Penny Tuppy's article here in notepad (don't print from this site, copy and paste into notepad) and leave it on your desk highlighting the points YOU want HER to hear...

Don't give her the article or even mention it, just leave it on your desk in plain sight.