That's why this is such a good thriller, it gets you thinking all sorts of things.
Paula is certainly hiding a lot of secrets but that doesn't mean that she murdered Kay at the library site.
If Kay had really called Ellen would the police not have found that call?
Nobody has actually asked exactly what Kay said, and although somebody asked Ellen about it, Ellen did not tell them what Kay said to her.
I think there are three different things going on, Ellen is over suspicious, has past mental problems and is very upset about Paula being maybe better than her at the job.
Paula has lost a child, has mental problems and wants the whole world to like her and needs to succeed.
Somebody did push Kay to her death, and David is having an affair with somebody.