Let us remember that these quotes come at the end of the first section of this short story, when Eveline remembers her mother and the fate that she suffered. What is key to focus on is the way that the memory of her mother, and in particular the way that she died, uttering her legacy to Eveline in the Gaelic words "Derevaun Seraun! Derevaun Seraun!" which means "The end of pleasure is pain," it is this that finally gives her the courage to actually move from her position of gazing vacantly out of her window and to stand up and leave. As she contemplates her mother and "her life of commonplace sacrifices closing in final craziness," she recognises that this is the path that she will take as well if she does not leave, and the second quote you have highlighted shows her internal conflict as she reasons with herself, trying to justify her decision to leave and persuade herself to go. Consider the longer quote:

She stood up in a sudden impulse of terror. Escape! She must escape! Frank would save her. He would give her life, perhaps love, too. But she wanted to live. Why should she be unhappy? She had a right to happiness. Frank would take her in his arms, fold her in his arms. He would save her.

It is the memory of her mother then that makes her feel "terror," and it is this terror that makes her stand up, looking for an escape from a future as a drudge and a death that will fulfil her mother's final words.

In spite of these quotes however, she finds herself unable to extricate herself from her religion and the call of duty on her life. When she finally comes to the crucial moment of leaving with Frank, she is only able to grasp onto the handrail in a state of paralysis as she watches him go, recognising that she must submit passively to her God and to her duty.