For Anna, there is an internal resolution as her mental processes undergo a shift in philosophical outlook. She comes to view her desirable affair with its undesirable spiritual and psychological affects as a "true" marriage, thus ridding herself of her most torturous internal suffering. Whether the gentleman in question will agree to the new perspective is more dubious.
Yes, I agree with #2 in that Oates gives us a rather depressing ending and one that we doubt is actually a resolution in the sense that we normally refer to in terms of conflicts being resolved. Clearly, the biggest conflict that Anna faces is an internal one, as she struggles between the shame of committing adultery but also the way that her marriage is dead and does not satisfy her needs. However, her decision at the end to entrust herself to a relationship that is based on physical love alone is a somewhat problematic ending. Throughout this excellent story, there is no sense of a relationship that is based on anything except physical longing between Anna and her lover, and so we are left wondering if this decision will leave Anna in a similar relationship down the line as she has with her present husband.
In Joyce Carol Oates' "The Lady with the Pet Dog," the resolution to the conflict is a weak one (for her character). Anna first decides that she is unhappy with her marriage and her adulterous affair. She concludes that she will never be able to have a life with her lover...
However, by the end of the story, much to her lover's surprise, she is filled with the conviction that she and her lover will live together in something like a "true" marriage. This seems to provide a resolution to her conflict as she searches for happiness and an answer as to which path she should follow in her life: she chooses her lover.
Although this would appear to offer a resolution for Anna's character, the resolution is as solid as a house of cards. Anna and her lover really don't know each other—their connection is more physical. Anna is deciding to go with her lover not because she has made a logical and intelligent decision: she goes with him because she believes that he will make her complete. A woman who was ready to kill herself at one point has rapidly changed her mind, has pulled herself together, and is ready to gamble her future on a man who is nothing as she imagines him to be.
There may well be a resolution, but it is not a healthy one for Anna.