Does Keima's mother know Elsie and/or Haqua's real identity?
I'm not aware of any further canon details or Word of God explanations, though I won't guarantee the latter doesn't exist.  

There would be a difference between "knows her true identity, ie that she is a spiritual being from Hell", and "knows that she's not really her husband's daughter (but otherwise just assumes she's a human girl with feelings for her son)".  

She probably just goes along with it in the end because she's ecstatic that her introverted NEET son is suddenly bringing (real) girls home with him, and she wants to give him some privacy and a chance to break out of his shell so he can establish real relationships with real people.  She is shown at various points worrying about Keima's future, and that he would come home married to a cardboard cutout one day and just go crazy-hobo mode.  As such it's consistent for her to jump at any chance to get Keima interacting regularly with a girl his age.