Describe the relationship between Tom and Mrs. Walker.
Take a look at her description in the second paragraph:
Tom's wife was a tall termagant, fierce of temper, loud of tongue, and strong of arm. Her voice was often heard in wordy warfare with her husband; and his face sometimes showed signs that their conflicts were not confined to words.
Termagant is a word that was used to describe a horrible, mean woman. From this description, it is obvious that she has a temper, yells quite often, and sometimes hits him. However, their relationship is fairly mutal, as is described earlier in the second paragraph:
He had a wife as miserly as himself; they were so miserly that they even conspired to cheat each other. Whatever the woman could lay hands on she hid away: a hen could not cackle but she was on the alert to secure the new-laid egg. Her husband was continually prying about to detect her secret hoards, and many and fierce were the conflicts that took place about what ought to have been common property.
They are both selfish and cheating one another by hiding away things for themselves that should be shared between husband and wife. It's pretty obvious that they don't have a very loving or trusting relationship.