Experts said such situations can remind parents to be aware of negative emotions like anger toward their children and pay attention to possible warning signs that their feelings are irrational.
"When parents feel consumed by their anger and cannot think about or feel any positive emotions toward their children, this is very concerning," said Nadine Kaslow, professor of psychology at Emory University in Atlanta. "If parents start to have fantasies of their children being dead or actually of killing them, not only do they need to step back but they need to get help."
There also are signs that it's time for a parent to step back and take a few deep breaths or count to 10.
Those signs may include, "when they feel that they are on the verge of saying or doing something they may regret [or] when they seem to be on the verge of forgetting that they are parents and not siblings to their children," said Dr. Harold Bursztajn, associate clinical professor of psychiatry at Harvard Medical School.
While she never wanted to kill her son, another woman told ABC News she had trouble bonding with him and often raised her voice and argued with him.
Her son, now 6, recently was diagnosed with attention deficit disorder.
His mother said he was sometimes a difficult child. She adopted him when he was an infant shortly after her biological infant son died.
"It was a combination of grief and a lack of bonding, and I got angry at him a lot," she said. "He would do things that little boys do, like leave the toilet seat up or leave dirty clothes on the floor. I would lose patience and argue with him. There were a lot of raised voices and I had a short fuse."
Experts say arguing is particularly problematic when dealing with adolescents. Instead, parents should tell their child they're too angry to discuss a certain issue.
Kaslow said there are other warning signs parents never should ignore, including neglect or abuse of their own children, thoughts about killing their children, saying they wish their children were dead and actual attempts to kill their children.
The mothers who spoke to ABC News want to encourage other parents to address their anger and get help, if needed. One of them, while she did get counseling and is able to cope with her young daughter's troublesome behavior caused by sensory processing disorder, still is struggling.
"I often feel like a horrible failure as a mom," she said, "because I can't seem to love my daughter like other people love their children."