The Ostensibly Singular "Each" and Possessive Form?

"Each" is indeed singular. "Of my parents' houses" is a prepositional phrase, and it doesn't affect the subject, which remains singular. You have two parents, and both of them have a house. "Parents'" is a possessive adjective for "houses," which is the object of the preposition "of." The thing is on standardized tests you have to remember that a prepositional phrase isn't part of the subject.