Eveline's observations and memories suggest that her father is not a positive figure in her life. He does not contribute to her well-being, and his violent nature and drunkenness, among other factors, make Eveline's life in Dublin unbearable.
First of all, Eveline's observations reveal that her father is verbally abusive, and she is afraid that verbal abuse could turn into physical abuse. Eveline feels threatened by her father. He would beat Eveline's brother and the only reason he would not be violent towards her was because she is a girl. With one of her brothers being dead and the other one living far away, Eveline feels at risk of being physically abused:
She sometimes felt herself in danger of her father's violence. She knew it was that that had given her the palpitations. When they were growing up he had never gone for her like he used to go for Harry and Ernest, because she was a girl but latterly he had begun to threaten her and say what he would do to her only for her dead mother's sake.
Textual clues suggest that Eveline's father is irresponsible and cannot rely on himself, so he needs someone who could perform his wife's duties, since his wife is dead, that person is Eveline, of course.
Eveline struggles to make her father contribute to making their lives easier because he does not wish to give his money to her to buy things which are necessary. He would rather spend his money on buying alcohol. He would criticize her by saying how she would squander his money:
He said she used to squander the money, that she had no head, that he wasn't going to give her his hard-earned money to throw about the streets, and much more, for he was usually fairly bad on Saturday night.
Eventually, he would give her the money, however, all this struggle would wear Eveline out, and this is one of the many reasons why she wishes to escape with her lover, Frank, to Argentina.