"I would question why a preacher's wife would want to attend a different church, however."
Because she (actually, the spouse isn't always "she") need her own pastor, just like the doctor's wife needs her own doctor. Generally, doctors don't practice on their family members, and clergy should take the hint.
Second, she needs her own faith community where she is "just a member of the congregation." This is impossible when they are the spouse of the pastor. Just try praying when the people in the next pew are making fun of the pastor for a gaff.....
"actually, the spouse isn't always she"
True. Joyce Meyer has been successfully married for some 40 years despite having the atypical relationship where she is up front in public ministry and Dave is more "behind the scenes." Less visible doesn't mean any less important.