After reading this thread, it seems to me that the royal family at Christmas faces the same kind of challenging issues that most modern families face at such times. In the WWII years, it was so easy. There was the King, Queen, and the two princesses with their dogs. Even into the 50s and 60s, it was still straightforward: the Queen, Queen Mother, Queen's husband and children, Queen's sister and her husband and kids. But then something happened. Divorces, remarriages, kids from other marriages who want to spend Christmas with their non-royal side of the family. The "family" is now a multitude of families much more complicated, diverse. It's classically illustrated in the case of the Kennedy family. When Big Joe and Rose were around and kicking, they were the Kennedys. Then Big Joe and Rose's kids grow up and marry. Their kids and grandkids are Lawfords and Shrivers and Smiths. Then even the Kennedy named kids marry Schlossbergs, Cuomos, Schwarzeneggers, etc.
I think that if Camilla's kids wanted to spend time at Sandringham with her and Charles, William and Harry, then The Queen would likely be happy to invite them for a day or two, but the case is probably as simple as: Tom and Laura prefer to spend the holidays with their dad's family or their spouses' families. And so Camilla makes time to go to them instead of them going to her. This is what most families have to do. It's impossible to see everyone you wish to see on the holidays. You try and you see who you can see, but it's all you can do, and there is always next year, we hope!!