Prince William and Kate Middleton do not have legal custody of their three children -- Prince George, Princess Charlotte and Prince Louis until they are adults. This is apparently based on a 300-year-old royal decree that has never been changed.
According to royal expert Marlene Koenig, King George I created a law in the early 1700s that would make the sovereign the legal guardian of the minor grandchildren. In 1772, the law was legislated yet again and was never changed since then.
Apparently, King George I did not have a good relationship with his son, the future King George II, George Augustus, so he created such a law. He banished his son and his wife, Caroline, from St. James Palace but their children remained with His Majesty.
As the law is still existing, this means that when Prince Charles becomes the King of England, he will have legal custody over George, Charlotte, and Louis as minors. Prince Charles will also have the same legal custody over Prince Harry and Meghan Markle's son, Archie Harrison.
As the legal guardian, this will give Prince Charles the right to decide on the minor grandchildren's education, travel plans, and even their upbringing. During King George I's reign, he even had a say on who the grandchildren could marry when the right time came.
In the 1980s, the law was in full force when Prince Charles and Princess Diana had to ask Queen Elizabeth's permission if they wanted to bring along William and Harry, then minors, for their travels. At one point, the Queen apparently refused Princess Diana's request to bring her children to Australia when her marriage to Prince Charles broke down.
Koenig also said that following the divorce of Prince Charles and Princess Diana, the custody of the children was never on the table since the Wales do not have the legal right over the kids. It was the same arrangement for Prince Andrew and Sarah Ferguson's divorce in the 1990s as Queen Elizabeth was also recognized as the legal guardian of then minors Princess Beatrice and Princess Eugenie.
In an interview with The Independent, however, Koenig said that the Queen generally had her grown children raise their kids and never interfered except when absolutely necessary. It's unclear, however, if Her Majesty also has the same legal custody over George, Charlotte, Louis and their minor cousins since the original creator of the law didn't have great-grandchildren.
