Connie Busby told the Aurora (Ill.) Beacon News the ship made it to port at South Georgia Island near the Antarctic Peninsula April 10 but could go no further because of a power failure.
Her father, Bob Bonifas, 74, said passengers on the Plancius, a 291-foot former oceanographic research vessel, have been told they will be back in Montevideo, Uruguay, April 24.
The ship's power troubles began 12 days into a planned 31-day journey, Bonifas told his daughter by satellite phone.
"We were out on an island seeing birds on a different island, and when we got back to the ship, (the ship sustained) a power failure," Bonifas said.
He said the crew managed to fix that problem but then the ship suffered engine failure.
A chartered passenger vessel from Argentina is headed to the Plancius to rescue the stranded passengers.
Celebrity Couples of 2014 [PHOTOS]