What powers does the British monarch have over the Royal family?

I recently finished a biography of Caroline of Brunswick. In one chapter theres mention of the possibily of King George III removing her daughter, Princess Charlotte of Wales, from her the custody of her husband, the future George IV, on the grounds that the sovereign has superior rights (even greater than those of a father) over members of the Royal family. I mentions precedence from 1717, but doesn’t elaborate. What was the author talking about? What special powers does/did the monarch have over the Royal family. I know the Queen must consent for royal marriages and has control over titles, but what else? Could she intervene in a child custody dispute (say to ensure the royal parent get’s custody)?