Aylsworth has said in court documents that when he told Marks he was going to stay with his wife, she cut off his visits with the children, forcing him to go to court to get visitation rights.
Marks says she never tried to stop him from seeing the girls. "He is their father. And I expect the children to love him, of course," she told Primetime.
But Marks also says she thought Aylsworth was rough with the children and had kissed them inappropriately, so she asked the court to order a supervisor be present for all his visits.
Aylsworth responded by raising his demand from visitation rights to full custody of the twins.
Later, Marks said one of her daughters told her Aylsworth had touched her genitals during a trip to the bathroom.
Marks had her daughters examined, and it turned out they both had mild vaginitis, a swelling and redness that experts say can be caused by many things — from inappropriate sexual contact to innocent bubble baths.
She also took them to see child psychiatrist Celia Blumenthal, who said she "60 to 70 percent" thought the girls had been molested.
Rock and a Hard Place
However, the police investigated and determined there wasn't enough evidence to press charges.
A forensic psychologist and social worker, both appointed by the family court judge, testified that they believed Marks coached the girls to say their father had touched them inappropriately.
Marks defended herself to Primetime: "If I don't report it, I'm neglectful and I should lose my children. And if I do report it, I'm a coaching brainwasher."
The court heard from 32 witnesses during 14 days of hearings. While there was no testimony that Marks had ever physically abused or neglected the girls, several experts testified that Marks was "unable to foster a positive relationship" between the twins and their father. One said she even put the girls in "psychiatric distress" around visits with Aylsworth.
Judge Goldberg decided the girls would no longer live with their mother, and gave their father full custody.
"The mother's failings … her unbridled anger towards the father and inability to foster the paternal relationship make her ill-suited to be the custodial parent of the children," Goldberg's opinion read.
But Marks was not about to give up without a fight. Up until the day Aylsworth was scheduled to pick up the twins, she sought a temporary stay.
She asserted that the court-appointed forensic expert was not impartial, noting his own brother had been involved in a painful custody battle and that he had not talked to anyone on her side of the family. But she conceded he had a lengthy interview with her.
The temporary stay never came. Instead, Aylsworth showed up at Marks' apartment building, accompanied by a social worker.
In front of the media gathered outside her door, Marks shouted at Aylsworth and the social worker to stop pulling the girls along. She complained that the girls' car seats weren't fastened. She threatened the social worker with a lawsuit.
She told a reporter she was going to "fight like a warrior for my daughters," to get them back from "these animals." And when Aylsworth's car finally pulled away with her daughters inside, Marks chased the car, yelling, "I love you."
Aylsworth's lawyers say Marks' behavior that day is evidence she doesn't have the best interest of the children at heart.
But Marks called the lawyers "inhuman and wrong. When mothers lose their children, they scream."