Sebastian: That's it. I'm booking meself on a cruise.
Melody: Do I have to do this? Everybody thinks I'm weird.
Ariel: We have to keep Melody away from her. Until Morgana is found Melody can't go in the sea.
Flounder: But Ariel.
Ariel: I'm sorry Flounder, but if Morgana is anything like Ursula, she will never give up. This is the only way. Melody can't know about merpeople or Atlantica or even about you, Daddy.
King Triton: Very well, Ariel, you're right.
Melody: What a totally cool feeling.
Answer: King of the Sea does not mean psychic powers that allow him to be able to snuff out everyone's location. Only power he has is through the trident, which obviously cannot pinpoint location as he couldn't find Ariel when she was missing. It's likely the humans have no idea of the family's mermaid history, because yes, the snotty kids probably would have greatly teased Melody for it.