Southwest Airlines spokeswoman Christi Day said the family was told Monday that the full cost of their one-way tickets from Detroit to Seattle with a stopover in Phoenix will be refunded after they were not allowed on a plane in Phoenix, KPHO-TV, Phoenix, reported Tuesday.

"I am furious about it," Wendy Slaughter, whose family was removed from the plane, said after arriving home in Seattle. "I just couldn't believe they could do something like that, and then, leave us completely stranded with no money and no way to get anywhere."

Slaughter said the flight marked the first time her children -- Henry, who suffers from autism, and Gracie, who suffers from cerebral palsy -- had been on an airplane and the experience made them excitable.

"The children were a little bit out of control on the flight. They were restless and excited and worked up, and they're kids."

However, the airline said the ruckus-causing kids were too much for the flight crew to handle.

"And for the safety of our customers and flight crew decided to not allow them to travel on to Seattle at that time," Day said. "Typically if it's a threatening behavior, it's not safe to travel at 30,000 feet in the air in a contained environment."