Ariel's Beginning is indeed a 3rd Little Mermaid movie. It shows Ariel as a little girl and then as an early teenager. It deals largely with how music became an integral part of Ariel's life. It's no comparison to The Little Mermaid, but it is actually pretty good as far as direct to dvd sequels go. Better than the 2nd which was essentially the 1st in reverse.
If you're a Little Mermaid fan, I would recommend seeing it. It's cute, the animation isn't totally bad. The villain isn't stellar, but oh well. One of the last direct to DVD so we can forgive it that.
Our revels now are ended. These our actors, As I foretold you, were all spirits and Are melted into air, into thin air: And, like the baseless fabric of this vision, The cloud-capp'd towers, the gorgeous palaces, The solemn temples, the great globe itself, Yea, all which it inherit, shall dissolve And, like this insubstantial pageant faded, Leave not a rack behind. We are such stuff As dreams are made on, and our little life Is rounded with a sleep. mycroft16 on Twitter