With every canoe hauled beyond her reach, Hinemoa was left facing the lake with no vessel and, by any reasonable measure, no way across. Mokoia sits well out from the Ōwhata shore, far enough that the swim is a serious undertaking even for a strong swimmer in daylight, let alone at night, in cold water, alone. Most tellings agree she did not decide this lightly or on a sudden impulse. She had already spent enough nights listening to know exactly what she wanted, and she had already exhausted the sanctioned paths to it. What was left was her own body and whatever she could find to help it.
What she found were hue — dry gourds, empty and sealed, light enough to float and buoyant enough that lashed under each arm they could hold a swimmer up through fatigue that would otherwise have pulled her under partway across. This is one of the details that makes the story feel real rather than simply admirable from a safe distance. She did not swim the lake through sheer will alone, the way the story sometimes gets flattened into. She thought about the actual mechanics of staying afloat for a long, cold distance, and she solved that problem with what was on hand before she ever stepped into the water.
Then, at night, she went in. There was no path laid out for her across open water, nothing marking the way except the one thing that had been reaching her from Mokoia all along — the sound of Tūtānekai's kōauau (small flute), still being played out across the lake the way it had every other evening, this time without either of them knowing it was finally being answered. She swam toward that sound, using it the way a sailor uses a fixed point, correcting her direction by ear in the dark when there was nothing to see and nothing else to steer by.
It is worth pausing on how long and how cold that crossing actually is, because the story does not ask you to imagine it as effortless or magical. She would have tired. The water would have worked at her the whole way. The gourds under her arms were not a guarantee, only an aid, and she still had to keep her own limbs moving through the whole distance with no one there to help her and no way to call for rest. What got her across was a combination of a practical solution, sustained physical effort, and the fact that the sound she was swimming toward never stopped — Tūtānekai had no idea he was guiding her, and simply kept playing the way he always did, and that ordinary faithfulness turned out to be exactly what she needed.
When she finally reached Mokoia, she was cold through and exhausted in a way that a person does not recover from instantly just because they have arrived somewhere. She made her way to a hot spring at the island's edge, a natural pool warmed from below, and lowered herself into it to bring the life back into her body before she went any further or let anyone see her in the state the crossing had left her in. That pool is still spoken of today, at the place where she is said to have first stepped onto Mokoia's shore, cold and shaking and finally, after everything, on the same island as the flute she had been listening to for so many nights.
Notice what actually got her there: not one heroic instant, but a whole chain of ordinary, deliberate choices — finding the gourds, going in at night despite the cold, correcting course by sound alone, refusing to turn back partway. If there is a barrier in front of you that everyone else has agreed is simply the end of the matter, it is worth remembering that Hinemoa did not out-argue her family. She solved the actual physical problem in front of her, one decision at a time, and let the crossing itself be her answer.