I really do not believe that Billie knows what happened to her daughter and hope I am not proved wrong. As far as checking on her in the bed, I don't even believe she did this, I think she said she did because NG was asking her in such a way, she felt she had to say it, and that is why her answer was so awkward.
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If a mother is going to leave the house and their children are sleeping, don't most look into their room? I would think this would be a fairly common event each morning just to make sure your children are safely tucked away. And since that was Hailey's room where she slept, why would she go shake her, touch her or anything else? She saw her sleeping and that was good enough for her.