Woods' arrest on May 29 has prompted her to consider applying for full custody of the children, they claimed.
The Jupiter Medical Center declined to comment on his reported stay on Monday and lawyers involved in negotiating his custody agreement with Nordegren did not respond to requests.
Woods' long-term agent Mark Steinberg also declined to address the reports.
According to the Radar Online source, Woods visited the rehab center with his children on June 2 and signed up for treatment days later.
Exactly how much Swedish Nordegren was awarded in their settlement remains contested. At the time, Fox claimed she was given $750million in exchange for agreeing to never talk about their marriage publicly.
That figure was lessened to $100million by other outlets including Forbes. Their divorce came after a parade of women including strippers and prostitutes revealed themselves as mistresses of the then untouchable golf star.
Afterwards, Woods checked himself in to the Pine Grove Rehabilitation Center in Hattiesburg, Mississippi, for sex addiction treatment.
Later, he received treatment for Vicodin addiction at The Meadows in Arizona.
Woods was arrested by the side of the road on May 29 near his mansion in Jupiter.
He had taken a cocktail of prescription drugs when police found him asleep inside his damaged $220,000 Mercedes with the engine running.
The 41-year-old was then filmed swaying in the street and slurring his words as he tried to take part in field sobriety tests.
He was later taken to a Jupiter police station where he struggled to blow into a breathalyzer and fell asleep on a chair while he was being processed.
Though he had no alcohol in his system, Woods had taken Soloxex, Vicodin, Torix and Vioxx - four different prescription drugs. In a statement after his arrest, he said his sleepy state was an adverse reaction to them.
'What happened was an unexpected reaction to prescribed medications," Woods said in the statement. I didn't realize the mix of medications had affected me so strongly.
'I understand the severity of what I did and I take full responsibility for my actions, I want the public to know that alcohol was not involved,' he said.
He also apologized to his family and friends, adding: 'I expect more from myself too.
'I will do everything in my power to ensure this never happens again.'
His first court appearance is scheduled for July 5. If convicted, he could face up to six months in prison and fees of up to $1,000.
In a blog post published days before his arrest, the golfer described how he'd been enjoying spending time with his children after undergoing fusion surgery on his back.
'I haven't felt this good in years,' he wrote, later explaining that he was in no rush to return to the sport competitively.
'I'm walking and doing my exercises, and taking my kids to and from school. All I can do is take it day by day. There's no hurry,' he said.
