I just remembered this fantastic thing called "Kid's night on Broadway."
It's on February 3rd and 4th, and after February, the first Tuesday and Wednesday of every month will have this deal.
Kids 6-18 can see any participating Broadway show for FREE as long as the adult with them pays full price. I just checked the list - and The Little Mermaid is participating in it.
I'm not sure if you're willing/wanting to wait until February to see it, but this is a really great deal if you are!
Here's some more info:
Kids Night On Broadway - Kids Go Free