Four episodes of the series were released on VHS under the title Ariel's Songs and Stories, a special "Princess Collection" that was exclusive to Ariel and Jasmine. In this video, the episodes contained an opening song and sequence that was different from the regular tv airings. This is that song. I actually quite like it, perhaps because the singer has a Jem and the Holograms vibe going on.

There's a special place where dreams come true
In a kingdom far away
Where a little mermaid calls to you
Please come on out and play

Let's play princess
Splashing around and around
Let's play princess
Sharing the treasures
And happiness we've found

What a feeling
Having a great time
Swimming through caves
Even riding the waves

Let's play princess
Making some wonderful friends
Let's play princess
In our magical world
Adventure never ends

What a feeling
Laughing and singing
All that we do is exciting and new
So let's play princess
The whole day through
(Let's play princess)
Come on, let's play princess
The whole day through