Is it okay for the little sister to experience the feelings of sadness, jealousy or anger about her older sister's successes?
Yes.
Those feelings are not morally wrong.11
They are the result of desiring a good thing (success) and not possessing it.12
Why do you think that the monster begin as little monsters and then become one big monster?
When the little girl wrote many times “I hate you”, she was deliberately willing evil upon her sister, which created little uncontrollable monsters.
Those ‘monsters’ represented a growing disposition toward evil which became a big, sinful desire to seriously wound or kill her sister.
What was the solution to stop the big monster?
The solution was to experience her feelings of sorrow/sadness (she cried on her sister’s shoulder), seek forgiveness, and choose to love her sister.
What could have been done in the first place to help the little girl avoid the little monsters?
Her parents and older sister should have paid more caring attention to her. That attention is really loving her by knowing her, and knowing how she is feeling. If they had done this, they would have also noticed the outward signs of her emotions and then been able to encourage her to feel, reveal and deal with them.
She needed to be patiently taught how to redirect her sad and angry feelings toward seeking the good things that God did have in mind for her.13
There are good things in life that we want and cannot have, or cannot have right away. Even so, God ALWAYS gives us the desire and the ability to attain the good things He wants us to have.14