She has been claiming HoH in previous years even though she does not qualify?

("Well, I have two kids 26% of the time, isn't that the same as one kid 52%?")

Now you know why she was looking for a new preparer.  The last one decided to come clean. 

And why the ex hasn't been signing an 8332. It wasn't needed if she was claiming a kid lived with her. 

Have you told her what she has been doing wrong?  Might be, the last preparer thought it up but has now been put out of business.