"Robert usually Skypes with us from his home office, which is where he did the interview.
"The kids probably heard voices coming from the computer and assumed it was us," she said laughing. "It was just hilarious."
Mrs Kelly, 72, explained that her 44-year-old son, who is an expert on South Korean politics, has done a number of interviews on network television for other outlets, including CNN, as well as CNBC, Sky News, and ITN.
She said: "I just hope that he gains recognition for his expertise rather than for this — as great as it all is."
Professor Kelly moved to Korea in 2008 to teach political science at Pusan National University, after completing his PhD at Ohio State University.
While at Ohio State he made friends with a Korean student who sparked his interest in the country's politics, his mother said.
And soon after making the move, he met his now-wife of six years, Jung-a Kim, a yoga teacher.
"We've been to Korea twice," said Mrs Kelly.
"First for Robert's wedding in 2010 and then when our granddaughter Marion turned 100 days old."
'Baek-il' is a Korean tradition, where families celebrate the 100th day of a child's life.
"I can only say "thank you' in Korean", said Mrs Kelly, "but I'm slowly learning.'
One of three children, Professor Kelly is "almost" fluent in Korean, his mother explained, but is "naturally good" with languages. He also speaks German, French, Russian, Latin and classical Greek.
The proud mom said that she first heard the video had "gone viral" when her sister called her this morning.
She said: "First my sister called and then we spoke to Robert, who was a little disturbed — probably just embarrassed."
Mrs Kelly added that she thought "the best part" of the video was when his wife, Jung-a, came skidding through.
In an attempt to salvage the interview, Jung-a grabs the two youngsters and drags them out of the room, but one of them could be heard wailing in the background and baby James' walker wouldn't fit back through the door.
"It was just fantastic," Mrs Kelly said. "Robert will be in for a real treat when he wakes up the morning."
As Korea is 14 hours ahead of the US, Mrs Kelly doesn't know if her son is fully aware of his internet fame — most of which grew when he would normally be asleep.
But Facebook posts on the professor's wall, congratulating him on his "performance" and calling him a "star", are flooding in.
One Facebook friend, Bobby McGill, wrote: "An instant classic. Be sure to get your book deal by mid-week."
Mrs Kelly told DailyMail.com that she is exceptionally proud of her son and all of his accomplishments, and added that he is a "wonderful" and committed father.
"Life happens," she said, laughing. "The lesson is to lock the door!"