A mother claims she was mistreated by United Airlines after she was forced to fly with her 25-pound son on her lap for three hours. Shirley Yamauchi had bought the 2-year-old his own seat costing nearly $1,000.

United blames a mistake at check-in that caused it to give the boy’s seat to a man on standby. His mother said the airline’s mistake caused her to worry about not only her son’s safety, but also her own, reports CBS News correspondent Kris Van Cleave.

“I was concerned for his safety,” Yamauchi said. “I had to attempt to put his seatbelt over him for the two of us, and it was very difficult. … He’s so big, I couldn’t put down the folding table. I put the drinks on my armrest. I knocked down the drinks with my elbow.”

Yamauchi and her son Taizo were waiting to take off on a Houston-to-Boston flight at the end of a marathon day of traveling that started in Hawaii when a man who had been on stand-by said her son was in his seat — the same seat her son had a ticket for. Yamauchi said she complained to the flight attendant.

“She gave me a short answer saying that the flight was full and she shrugged and she walked away,” Yamauchi said.

Yamauchi considered protesting further but said she was afraid of retaliation after Dr. David Dao was forcibly removed from an overbooked United flight when he refused to give up his seat.

“I thought about Dr. Dao and his incident with United, having his teeth knocked out and being dragged down the aisle,” Yamauchi said. “And I didn’t want that to happen to me.”

She did complain after arriving in Boston, but it wasn’t until five days later – long after her husband posted pictures on social media – that United apologized, saying there was a mistake scanning the boy’s boarding pass that made it appear he was not checked into the flight.

“We deeply apologize to Ms. Yamauchi and her son for this experience. We are refunding her son’s ticket and providing a travel voucher,” United said in a statement.

“It doesn’t feel genuine. It’s forced upon them. They’re trying to fix their image or save their reputation,” Yamauchi said.

United has now apologized directly to Yamauchi and said it’s working with its employees to prevent a repeat of the situation. The FAA strongly advises against parents holding children in their laps and airlines require children over two to be in their own seats and not on a parent’s lap.© 2017 CBS Interactive Inc. All Rights Reserved.