Gun for a Coward

Gun for a Coward is a movie starring Fred MacMurray, Jeffrey Hunter, and Janice Rule. After the death of a rancher his three sons run the ranch but one of them is seen as a coward because of his reluctance to gunfight.
A young cowboy, whose dedication to the principles of peace and reason has earned him a reputation for cowardice, overcomes his psychological aversion to violence after his elder brother unjustly censures him for not joining in a foolhardy gunfight in which their youngest brother is killed.