Can I move someone else's dolphin?
Dolphins don't belong to anyone. In my version of the rules (UK), the only thing a Dolphin does is let you pay 3 movement points (I.E your entire turn) to move a swimmer and dolphin to the safety of a coral island, and leave the dolphin in front of the island.

You can move the dolphin with the swirler without having any effect on the swimmer(s) present.

I think different editions have different rules though.