Then you need to read up on sociopaths, psychopaths, and pathological narcissism. The common theme there is LACK OF EMPATHY.
The term premeditated is not quite applicable here. She was subject to compulsive thoughts, thoughts she could not avoid. I doubt that she pursued thoughts of killing JonBenet but rather she could not avoid them.
She may have treasured her daughter but she also crossed identity boundaries and included JonBenet's identity in her own. Patsy treasured JonBenet because the child was an object that carried the projection of a large part of Patsy's own identity. Patsy has to act the mourner because she has no empathy for anyone other than herself. She'll cry buckets at her own losses but will have to act the part when confronted with another's loss.
Patsy took JonBenet's life INTO her own. The girl is now an angel, not in heaven but rather in Patsy's fantasy. This is textbook stuff, read it; psychopathy, sociopathy, narcissism, borderline, READ IT!