Grover said his daughter had been shocked at seeing herself in such a state.
"She got a shock of her life and she's decided to change.
"All I can see is good things .. .like the phoenix rising from the ashes.''
The video - which has racked up to two million views - shows her in a comatose state alongside her boyfriend, who has also taken drugs.
The family had received a mix of feedback since the video was uploaded; mainly positive, but also negative reactions.
The woman's brother, Tuakeu, said he had no regrets posting the video; as he hoped it would motivate others - including his sister - to change.
"I don't want drugs to be part of her life ever. I want that to stop.
"That's why I hope she does this rehab - and hopefully it works.''