Rob Mowlam told his father the ship's crew had started giving away free alcohol to passengers.
"He was concerned about what that was going to lead to when people start drinking too much," Mowlam said.
Other passengers have described more dire conditions, including overflowing toilets and limited access to food.
Texas resident Brent Nutt, whose wife is on the cruise ship, said Monday that she told him the "whole boat stinks extremely bad" and some passengers were getting sick and throwing up. Nutt said his wife reported "water and feces all over the floor."
Carnival hasn't determined what caused the fire or how it caused the electrical problems that have crippled the ship's water and plumbing systems, said Oliva, the company spokeswoman.
The ship was originally going to be towed to the port in Progreso, Mexico, but after currents pushed it northward, a decision was made to take it to Mobile to make it easier for passengers without passports to get home, the company said.
A similar situation occurred on a Carnival cruise ship in November 2010. That vessel was also stranded for three days with 4,500 people aboard after a fire in the engine room. When the passengers disembarked in San Diego they described a nightmarish three days in the Pacific with limited food, power and bathroom access.
Carnival said in a statement that it had cancelled the Triumph's next two voyages scheduled to depart Monday and Saturday. Passengers aboard the stranded ship will also receive a full refund, the statement said.
Associated Press writers Michael Graczyk and Ramit Plushnick-Masti in Houston and David Warren in Dallas contributed to this report.