Just one tiny query on that, as I don't have my Sandringham and the Royals book handy. I know Queen Victoria insisted on all her children, grandchildren and their spouses and families spending Christmas with her at Windsor if they possibly could, but what about later royals? Did King George V invite his siblings and their families, and the Yorks and the Lascelles and Fifes to Sandringham Christmases? Did the Queen's father when monarch have the Kents, Gloucesters and the Princess Royal and family and also cousins from his father's side (the Fifes?) to stay each Christmastime? Or is this a reasonably new tradition, confined to this reign.
I'm not sure if you've mixed up the siblings of Georges V and VI or if I've misread your post, so I'm just going to add this to clarify who we're discussing:
George V's siblings were Albert Victor, Duke of Clarence (died in 1892), Louise, Princess Royal and Duchess of Fife, Victoria (never married), Maud, Queen of Norway, and Alexander (died at birth). His mother, Queen Alexandra, died in 1925. I don't know if Louise and her family did Christmas at Sandringham. I would assume that Victoria did - she lived with her mother up until her mother's death and is described as having been close with her brother. I would assume that as the wife of a foreign monarch, Maud did Christmas in Norway.
George VI's siblings were Edward VIII, Mary, Princess Royal and Countess of Harewood, Henry, Duke of Gloucester, George, Duke of Kent, and Prince John (died in 1919). His mother, Queen Mary, outlived him. I don't know about every year, but Kyle posted a picture of the last Christmas at Sandringham under George VI (in 1951). The then Duke and Duchess of Gloucester and Princess Marina, Duchess of Kent, their children (the Queen's cousins), and Queen Mary are all present. Not pictured is the Lascelles family so I'm not sure if they weren't there, or if they were there but were excluded from the photo.
This is a guess on my part, but I'm kind of inclined to believe that having at least most of the siblings if not necessarily all of the monarch and their children at Sandringham (or Windsor for the years it was done there) is something of a BRF tradition.