I agree, just come out and tell her. :/ There's never an easy way to tell someone that someone so personally close to them is gone. She may have hated her mom, but I don't truly believe you can ever hate the people that brought you into this world. :/ I hope everything goes alright.
one mama on here had to do the same thing a couple years ago. She just sat her down and told her. The little girl was 6 or 7. So she had to have some counseling and all that. There isn't any easy way to tell her that her momma isnt coming back