The Mermaid's Apprentice by C. L. Savage

Book 2 in the Mermaid Adventures Series

Follow Melanie as she learns what it takes to be a mermaid, and her apprentice Ri'Anne who wants to be a mermaid too. Not everything goes as planned. Sometimes falling out of airplanes without a parachute is the only way to go. Or, well, sit in the air if you can't find a decent chair. Sometimes it means trying out fairy wings. 

Each of these girls must determine for themselves who they really are, and what kind of a special person they want to be.

From the back cover

Melanie is a newly minted mermaid on her way to visit her Uncle Arlo, hoping to help him with his marine biology research and earn her tail. Along with Melanie on the trip is her dad and her friend Ri’Anne, who Melanie hopes will follow her in her footsteps to become a mermaid like her.

To teach another to be a mermaid takes magic and lots of water! Melanie’s plan is first to learn what it takes to be a mermaid, so she can teach Ri’Anne, all while doing research dives for her uncle. However, Ri’Anne is a fairy at heart, and while she wants to please Melanie, trouble can result when fairy meets water.

Will Ri’Anne choose to be a mermaid and fulfill her lifelong dream, or follow her heart and become a fairy and fly free? Can Melanie still fulfill her quest for a mermaid tail?