In the Salt Lake Tribune, a historian describes the circumstances. Brigham's grandson was indeed a murderer and it was pretty sensational too. You can read the details in this article and access a real New York Times article published in 1902 just after he was caught or this article as the trial begins.
Wikipedia is at odds with the Tribune account in some details.
The boy obviously had problems for a long time. What I find most interesting in the account are some details about the boy's father, John Willard Young, the son of Brigham Young. John Willard was ordained as an apostle of the Church but never placed in the Quorum of the 12 Apostles. If the succession rules had not been changed, John Willard may have become President of the Church. This is described in an article from Dialogue by historian Todd M. Compton.
John Willard served as a counselor in the First Presidency to his father, when Brigham was President. But, he was never put into the Quorum of the 12 Apostles. In addition, he seems to have spent little time in Church duties or in Utah. By all accounts he lived much of his life in New York City, where his son, William Hooper Young, committed the murder.