It is seen that she is jealous of Ai and get very angry when she sees Masao acting as a dog to Ai
Psychological point of view
(Based on Funimation's english dub)
Season 1 and 2 implied that she might had been abused by her father (Besides verbal hinting, She shows how she uses her Bunny's), Particularly happiness Bunny, inside herself to fill the "emptiness" she physically had taken away) and abused her, causing the high probability in her future to have complex post traumatic stress.
t'wards the end of seasons 2 to the beginning of 3, Nene's father has gone through counseling, Never to hurt Penny or her mother again. This Psychologically leaves Nene's "Auto Pilot"(or typical "comfort level" to survive) at a stand still. She has become so used to this, that she cannot mold a new healthy personality on her own, and admits to being so furious, being her only weapon to overcome her problems. (She is also 5/7 years old, and according to Penny's mother-in season 3-her insurance cannot pay for counselling so it is typical that she cannot break away from the habit ) It is also shown the same pattern with penny's mother.
This point of view has been disproven by an episode where Shin-chan and his sister gets to choose a new family before being born. There was one route where they chose Nene's family and based on that her father actually seemed very kind and loving towards his temporary children, so that father probably treats Nene lovingly too, but just doesn't get many appearances.