I agree. If the female character had been more important to the story (and if that character wasn't as hyper), then maybe the ending could've worked. But it wasn't all her fault.
Howard Hawks couldn't provide good roles (or good dialogue) for women. Red River is a great example. At the beginning of the movie there was another female character--Wayne's love interest. She was almost as annoying as the one that ruined the ending! Later, in the "Rio" Westerns that reunited Hawks with Wayne, he left out the women almost completely.
Rent or buy Conagher (Sam Elliott) or Hondo (coming out in DVD soon, John Wayne) or The Quick and the Dead (Sam Elliott, not the other one).
There you have women in the West done well by Louis L'Amour, author of the books they were made from.
The writers were often at fault when all they could think of for a woman to do was scream hysterically or chatter nervously.