Near the start of his older brother’s funeral, Donny Osmond stepped up to the pulpit of a Church of Jesus Christ of Latter-day Saints chapel in Orem, Utah, and shared a recent story about Alan he hoped would set the tone for the service.

Just two weeks earlier, Donny Osmond had been in Las Vegas, where he performs five nights a week, sitting in a room with one of Alan’s eight sons, David, and…