"She's a gift from God," says Barrett, who lives in Lexington, Miss.
Grace was conceived through very modern techniques. The embryo was created outside any human body and then frozen. Barrett provided the egg, and her husband at the time, Don McGill, had provided the sperm.
Then the situation got very complicated. Correspondent Bernie Goldberg reports on this tangled web of anger and love.
Barrett and McGill were married for 20 years; McGill was a terrible husband, according to Barrett. "It was a dysfunctional marriage," she said of their 20-year union, which ended in 1996.
The couple had three other children together during their marriage and shared custody of them following the divorce. But Barrett wanted this child to be hers. She implanted the embryos and gave birth to Grace after the divorce. Her plan: McGill would have no contact with the child.
But McGill, a 64-year-old millionaire car dealer who lives in Houston, wanted to be involved in Grace's life.
"She just will not let me be a father to Grace," he said. "How would anybody think that I would give one of my children away and keep three....We're talking about human beings here."
"Unfortunately, in the real world - circumstances where one parent is toxic, where one parent has nothing positive to give that child and only negative - and that's this case," said Barrett.
After the birth of their third child, Barrett had her tubes tied. But in 1994, the couple had agreed to create frozen embryos in case they ever wanted a fourth child. In 1996, a few months after getting divorced, Barrett had one of those embryos implanted into her uterus.
In one of the most unusual cases in American legal history, a suit filed before the Texas Supreme Court raised the question about the nature of fatherhood. McGill and his lawyers said that because he's the biological father, he has parental rights.
Barrett and her lawyers acknowledged that McGill is the biological father and the sperm and the egg were frozen while the couple was still married. But they said that because the embryo was implanted after they were divorced, and because Grace was born after the divorce, McGill had no more rights as a father than an anonymous sperm donor - which means no rights at all.
"He's the sperm donor, he's the sperm donor, he's the sperm donor," said Lynne Liberato, Barrett's lawyer.
"He's the daddy, the daddy, the daddy," said Roy W. Moore, McGill's attorney. "The mother cannot simply say, 'I don't want this child to have a father. I'm going to make this unilateral decision all by myself. The daddy doesn't get to see the child.' She can't do that."
As so often happens, the couple's divorce was acrimonious. McGill was an absentee father and an adulterer, Barrett said.
"He was emotionall distant," she said. "He was physically distant. And he was not there for the children. And when he was there, we were all walking on eggshells."
McGill admitted that he had affairs but adamantly said that he is a good father.
So why did Barrett use his sperm to have a baby? "I thought this was my one chance to have a child and raise a child in the absence of this terrible malice and sickness," she said.
Barrett said that McGill agreed to allow her to implant the embryos, with the understanding that he wanted no relationship with, or responsibility for, the child.
McGill said there was no agreement.
While Barrett was pregnant with Grace, she started dating Jim Schmit. They were married three months after Grace was born. According to Barrett, her remarriage triggered her ex-husband's sudden interest in Grace. Barret said that McGill told her that if she married Schmit, he would sue for custody.
McGill disagreed, saying that the trouble really started when he married someone else. "(Barrett) told me point blank (that) if I married Cathy, I'd never see Grace," McGill said.
Two courts have sided with McGill, giving him visitations with Grace. Every other weekend, he flies from Texas to Mississippi to see Grace.
McGill also pays $4,000 a month in child support. Barrett doesn't need the money and sends the check to a trust fund for Grace, she said.
McGill put so much pressure on her and her second husband over Grace that it led to a second divorce, Barrett said. Once again, she is a single mother.
Then, in April, Barrett and McGill's oldest son, 21-year-old Donald Jr., was killed in a car accident in Mississippi. His death devastated both of them.
It also radically altered their perspective over the court fight. "We don't get 'do-overs,'" says Barrett. "We just have to go from today and do the best we can for the children that we still have."
Suddenly their anger melted away. "I see her as a human being, a mother of my children," says McGill of Barrett.
"Don is suffering, and the hole in his heart is just as big as the hole in my heart," Barrett says of him.
Barrett dropped her court fight to terminate McGill's parental rights. "Don does not need to lose another child," she says. "It was the right thing to do, and I didn't hesitate."
They will now share custody of Grace.
Instead of accusations, they now offer advice for other parents in custody battles: Says McGill: "If anybody is fighting with their spouse about children, please stop for the children and for you."
"Don't waste a minute on anger or being right," says Barrett. "Be forgiving. Be forgiving of yourself, be forgiving of the other parent, and just love them."