I live with my wife and son. My parents live 3 blocks away and visit us monthly.
Is it a little bit unnatural to use visit here? They are my parents, not other relatives like aunt, niece and nephews.
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Since "visit" has many definitions related to "coming in order to spend time" then we can say that there is absolutely no difference in who is visiting whom.
Almost in all cases "to visit" means "to come and spend time with as a relative or guest", but it can also mean "to attend a place for admiration and (or) sightseeing" which is: