The character who represents Eveline's antagonist is her father, Mr. Hill.  Eveline feels trapped, mistreated, and unloved.  It is her drunken and abusive father that makes her feel this way.  He is overbearing and doesn't listen to her wants or needs.  Rather than discussing with Eveline the relationship she has with Frank and trying to reason with her about it, he forbids her to see him.  Part of why Eveline feels so trapped is that she has so many responsibilities.  Her father has squandered money.  He mistreated her mother to the point of driving her insane, and the suggestion is that this was the cause of her death.  It is on Eveline's shoulders "to keep the family together."  But she doesn't want to remain so long in her father's world to end up the same way as her mother.

The more abstract antagonist of this story is society, however.  Eveline is trapped by the traditions of the time period, which require women to be subservient to men and enforce "rules" of proper behavior.  These rules hinder Eveline's decision to leave with Frank, because it could be scandalous.  In a less retrictive environment, her decision would have been easier to make.