(CNN) -- The parents of slain Tennessee minister Matthew Winkler on Tuesday asked the state's Supreme Court to overturn a lower court's order giving his widow -- who was also his killer -- visitation rights with the couple's children.

Holding baby Brianna, Mary Winkler stands next to Matthew. In the foreground are Mary Alice and Patricia.

At the least, they want the visits to go on only under a counselor's supervision.

Mary Winkler was convicted earlier this year in the 2006 shotgun death of her husband, a Church of Christ minister.

She said his slaying came after years of abuse, including physical violence and being forced to dress "slutty" for undesirable sex acts.

Prosecutors were pushing for a first-degree murder conviction, but a jury convicted her on the lesser charge of voluntary manslaughter.

Winkler initially received a three-year sentence, but a judge required her to serve only 210 days and gave her credit for the five months she had already served behind bars.

The judge allowed Winkler to serve the remaining 60 days in a mental health facility. She was released in August.

Since her arrest, the Winklers' three daughters -- Patricia, Mary Alice and Brianna, who were ages 8, 6 and 1 at the time -- have been in the custody of Matthew Winkler's parents, Charles and Diane Winkler.

The Winklers are battling Mary Winkler for custody of the children and have also filed a $2 million wrongful death suit against her for their son's slaying.

In September, a lower court granted Mary Winkler visitation with her daughters, mandating that the visits be supervised by a guardian to represent the children's interests, as well as by the couple Mary Winkler is living with or her sister. A subsequent appeal by the Winklers was denied.

The Winklers requested that if a court grants visitation at all, it should be under the supervision of a professional counselor. Several experts who testified in a September hearing on the matter said as much, the Winklers said in their filing.

Also in September, witnesses testified the children "exhibit fear and confusion" toward their mother "and her role in their father's death," the Winklers said.

One expert quoted Patricia as saying her mother killed her father and "I don't know if she will kill me. I want to ask her if she would do that to me. It scares me, kind of; if she did, well, I guess I would see my father," according to court documents.

The Winklers also said that after telephone calls with their mother, the girls experienced "urination accidents, sleeping problems, graphic nightmares and sleepwalking. ... It is evident that the children will have difficulty reconnecting with [their mother]. If visitation is determined to be appropriate at all under these circumstances, it is in the children's best interests to have a professional counselor present."

The couple said the court made a mistake by not appointing a guardian until after the September hearing.

After the March 22, 2006, slaying of Matthew Winkler, Mary Winkler fled with the children to the Alabama coast, where she was arrested. She said during a September appearance on "The Oprah Winfrey Show" that she never expected to get away with killing her husband and she fled in order to be with her daughters and "have some good times."

She also said she did not think her sentence was long enough.

"There's no amount of time I think you can put on something like this. I was just ready for them to lock the door and throw away the key," Mary Winkler said.

During the trial, her former father-in-law testified that his son had never been violent.

Diane Winkler chastised Mary Winkler for never apologizing to his parents or children. During her Oprah appearance, Mary Winkler said she would like a chance to sit down with the Winklers, saying she loves them, misses them and prays for them daily.

Asked what she would say to them, Mary Winkler said she couldn't pare it down to two or three sentences. "Just when that time comes, my heart will tell me what to say," she said. E-mail to a friend

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