Elizabeth Edwards' Health Raises Custody Questions

June 1, 2010— -- Elizabeth Edwards, battling terminal breast cancer, will not burden her oldest daughter with looking after her other two young children if she dies, opening the door to the kids' being raised by John Edwards and his mistress.

In an e-mail to ABC News.com, Elizabeth Edwards emphatically denied a report that she was "grooming" daughter Cate, a 28-year-old Harvard-educated lawyer, to raise her younger siblings Emma, 12, and Jack, 10, in the event of her mother's death.

"The story is not true," Edwards said in reference to a New York Daily News story that cited unnamed sources saying she did not want her children raised by her husband, former Democratic vice-presidential candidate John Edwards.

Elizabeth Edwards denied that Cate or any other family members would get the children and said they would go to John.

She said the Daily News story was false and had "no source."

"The children would go to John and then, if he died, to Cate, that is what we always said in our wills," Edwards told ABC News.com.

Edwards' sister Nancy Sims told ABC News.com that Elizabeth had never asked her to take care of the children and knew of no plans for the custody to go to anyone other than John Edwards.

"I have no idea where they came up with the story that Elizabeth is trying to keep John from having custody," Sims said.

Sims also denied reports that Elizabeth Edwards had "taken a turn for the worse lately," as the Daily News reported.

"She's healthy right now. She's not dying. She's doing extremely well. She's undergoing treatment," Sims said.

Elizabeth Edwards continues to live with Emma and Jack in the North Carolina home she once shared with John Edwards.

Cate Edwards lives in Washington, D.C., and clerks for a federal judge in Alexandria, Va.

In 2004, Elizabeth Edwards announced she had been diagnosed with breast cancer on the day her husband and presidential running mate John Kerry conceded defeat. In March 2007, Edwards announced the cancer had returned and John would continue his bid for the presidency.

In January 2010, days after John Edwards admitted he had fathered a 2-year-old daughter with mistress Rielle Hunter, the couple announced they had separated and Elizabeth filed for divorce.

John Edwards Expects to Get Custody of Children

In a recent interview with Oprah Winfrey, Hunter said John Edwards provides child support to his daughter, but would not comment on whether she continued to maintain a relationship with him.

Wade Smith, a North Carolina criminal defense attorney representing John Edwards during an ongoing federal investigation into whether he misappropriated campaign funds to provide for Hunter, said he was unaware of any plans to attempt to deny John Edwards custody.

"It's not something I am aware of," Smith said.

In most cases, custody would automatically go to the father in the event that a divorced woman who had custody of her children died.