The three primary characters in Ethan Frome by Edith Wharton are Zenobia, Mattie Silver, and of course the title character, Ethan. As your question suggests, each of them does "engage in a process of replacement."
Zenobia, better known as Zeena, is a querulous and rather sickly woman. This is the most notable thing about her, and this supposed sickness is part of her replacement. The only reason she and Ethan are married is because she was there to nurse his sick mother.
When she is playing the role of nurse, Zeena is perfectly healthy; as soon as she has no one to care for, she becomes sickly. Unfortunately, she is sickly for most of her marriage until she is forced to nurse both Ethan and Mattie after the crash. She knows that Ethan does not love her, so she resorts to accepting his care and concern for her health as a replacement for his love.
We learn that Zeena does love Ethan primarily through the incident with the pickle dish. When she discovers that Mattie has both used and broken the red dish, Zeena dramatically responds to the loss.
"You...waited till my back was turned, and took the thing I set most store by of anything I've got, and wouldn't never use it, not even when the minister come to dinner, or Aunt Martha Pierce come over from Bettsbridge—" Zeena paused with a gasp, as if terrified by her own evocation of the sacrilege. "You're a bad girl, Mattie Silver, and I always known it. It's the way your father begun, and I was warned of it when I took you, and I tried to keep my things where you couldn't get at 'em—and now you've took from me the one I cared for most of all—"
Obviously Zeena is describing her broken marriage more than her broken pickle dish. Because she is unable to express her love and therefore her anguish at the loss of her husband's fidelity, Zeena replaces her love for Ethan with her expression of love for this ridiculous piece of glass.
Mattie is a young woman in desperate need when we first meet her and when she comes to stay with the Fromes. She is looking for stability and she thinks she finds that in Ethan. Ethan is stable in the sense that he is not going anywhere, but it is not because he wants to stay. She does not see that he feels trapped and is restless to leave; all she sees is that generations of Fromes have been buried on the family property, and Ethan is going to do the same. It is hard to know if Mattie really loved Ethan or if he is just someone she can count on and who will take care of her when no one else will. After the crash we do not see that love, so it seems as though she has replaced her love for her father with her love for Ethan.
Ethan is so miserable because he has always settled for something less, replacing finer things with lesser things. Rather than face a life of being alone after his mother died, he marries Zeena as a replacement for loneliness. Rather than pursue his interests in science, he settles for reading a science magazine the narrator leaves in his sled, replacing real possibilities and potential with mere dreams. Rather than try to find a way to be happy, he agrees to Mattie's scheme to commit a double suicide, replacing possible happiness with death or, as it turns out, a life worse than death.
Even the unnamed narrator of the story replaces the real story of Ethan and his life with the two women with what he calls a "vision of his story."