This episode is perhaps more interesting for its attitude about facial hair -- and a plot error that somehow escaped the script editor -- than it is for the story.
Mary Woodson (Joan Shawlee -- Sweet Sue in "Some Like It Hot") says she's spent her last money to come west. Yet in the final scene, she's ready to get on the stage -- without any explanation of where she obtained the fare. The other characters show no sympathy for her plight, and Milly "helpfully" offers the suggestion "I'm sure you'll find something." Indeed. This is as close as the episode comes to recognizing the realities of Western life.
The story would have worked better "straight", showing what would likely have happened to a woman with no money and no one willing to help her. (The "Gunsmoke" episode "Talbot" shows what happens to such women.) But you didn't discuss such things on 1961 TV -- especially not on a heart-warming "family" program about a trigger-happy rifle-slinger who kills almost everyone who threatens him or his.
Kay E. Kuter (playing Charve Banner) is one of those rare actors (including Arthur Hunnicut, Monty Woolley, and Denny Miller) who prefer(red) not to shave. As Men With Beards Are Not To Be Trusted, he's perfectly cast as ne'er-do-well who has a run-in with the immaculately groomed Lucas McCain. (In "Frasier" he was cast as a scruffy homeless man who, in exchange for the new location of a shoe store, demands a kiss from Martin Crane.)
It is this episode's /failure/ to come to grips with the situation at its center that would make it worth discussing with your children.