Why does the author allow the audience to understand what is happening with both families?
Thornton Wilder breaks a few traditional conventions in Our Town. First, he breaks down the fourth wall, or the imaginary dividing line between actors and audience. The Stage Manager addresses the audience, characters from the audience interact with actors, and two concurrent scenes run at once with no props or dividing walls.
Second, the play is not set up according to a "plot" triangle (Feytag's, Aristotle's, etc...). The acts run the course of a person's life: birth, daily life, marriage, and death. No major event, in terms of climax, leads to tragedy or comedy; in fact, Emily's death is like everything else, part of daily life.
Third, he plays around with time. We know how and when people will die as soon as they are introduced. We know that Act III will be about death before it happens. And, of course, Emily travels back in time in Act III. You can't do that without the Stage Manager.
Thornton Wilder presents both families to the audience THROUGH the Stage Manager; he must serve as a mediator, observer, participant, and narrator to serve as a common thread between all three acts. Godlike, omniscient, he is part of the eternal. He tells us of the action between the two families; otherwise, the family members will seem too universal and archetypal, and the play will just be plain unintelligible.
So, to answer your question, both families are presented on stage because Wilder wants to stress the universal and the experimental. Presenting one family would have been too individualistic, traditional, and corny--almost like a sitcom, or an episode from Little House on the Prairie. Two families, at once, back and forth--that's experimental, never done before. Staging both families not only shows duality in time and space, but it reveals a visually and intellectually experimental theatrical experience.