He said she was in a "better position" than they had thought and the family were "pretty happy".
"I think the main thing so far is they've only just managed to stabilise her. Up until now it's been pretty hairy."
Mr Hopkins said they had complete confidence in the medical team.
"Now that she is more stable they are able to attend to the burns a little more than they have been," he said.
"She's still a very sick little girl. She's doing her best, she really is. It's hard to watch, it's really hard to watch. We're just so helpless."
The Support for Arna Fund has been set up to help the family with travel and accommodation.
Mr Hopkins said fundraising efforts had helped bring the family together at Middlemore Hospital.
The other children were taken to Butterfly Creek for the morning while Arna was in surgery.
"For the rest of us, that is what we were working for - that they have the ability to be together as much as they can," said Mr Hopkins.
"That's really nice for them."
It seemed Arna was slowly making progress.
"It's just wait and see for everybody ... she's definitely going in the right direction," he said. "Arna's by no means out of the woods just yet."
Any donations can be made to: Support For Arna, National Bank a/c 06-0689-0298651-00