Camron,
Although I've never seen a player wear their shinguards/socks the way you describe, I don't see why it could be illegal. According to the
Laws of the Game (Law 4 The Players' Equipment), shinguards:[*]are covered entirely by the stockings;[*]are made of a suitable material (rubber, plastic, or similar substances);[*]provide a reasonable degree of protection.
As you describe the way your kids wear their shinguards and socks, I see no infringement to Law 4 as all three requirements are met.
Furthermore, Law 4 is
not included in the permitted modifications described in the Notes on the Laws of the Game. This means your club should not be allowed to introduce modifications to Law 4.
Bottom line: the ref was wrong.