Charlotte lost her arms and legs to meningitis as a baby in 2004 and needs ongoing assistance with prosthetic limbs as she grows.
Mrs Remington yesterday said the pair, who take turns at rowing and resting, had battled "massive seas and rogue waves" on their 6m mono-hull rowboat, the Spirit of Orlando, over the past two weeks.
One giant wave threw Mrs Remington into the bow, almost knocking her overboard. "I thought, 'My God, with 10 days to go we're going to capsize'."
A baby squid hurled on to the pair's vessel by a large wave also hit Mrs Remington in the chest, an Auckland University spokeswoman said.
"They killed it. I think the shock of being hurled on to the boat and at Tara stunned it. They're planning to use it as bait and try a bit of fishing," the spokeswoman said.
Hundreds of flying fish also added to the pair's experience, with the women being forced to dodge the leaping creatures while rowing.
Mrs Remington's wife Rebecca and two children, Jade and Seb, have flown to Hawaii to greet her.
The family, who spent Jade's 12th birthday apart because of Mrs Remington's absence, are looking forward to being reunited.
Mrs Remington, who left her native United States for New Zealand 18 years ago, became interested in ocean rowing after hearing a long-distance rower speak at a school she was teaching at.
She competed in her first ocean race - the Trans-Atlantic Rowing Race from the Canary Islands to the West Indies - in 2005 with fellow-teacher Iain Rudkin.
About 18 days into the row, a 3.5m shark battered the pair's boat for 15 minutes, and on the 47th day they began taking on water and were forced into their life raft.
Two years later, she helped set a world record for the race as part of a four-woman team.
Despite making good progress on her latest quest, Mrs Remington was devastated to hear of transtasman solo kayaker Scott Donaldson's rescue off the Taranaki Coast on Friday.
"My heart just breaks for him. I absolutely know what it's like."
Donations for the trip can be made at: www.tararemington.weebly.com
