LONDON — If much of the world was captivated by the life and death of Charlie Gard, the incurably ill British baby whose parents waged a legal war with a hospital over his treatment, for Stephanie Nimmo, it was deeply personal.

Like Charlie’s parents, Connie Yates and Chris Gard, Mrs. Nimmo had sought experimental treatment in the United States for her daughter, Daisy, who had a rare genetic condition called Costello syndrome that made her partly blind and unable to speak more than a few words. She, too, grappled with the promises of alluring but unproved medical research and the dizzying array of armchair diagnoses on the internet.

The two sick children were even treated at the same London hospital, Great Ormond Street, which opposed the Gards’ court petition to pursue treatment abroad and, later, to bring Charlie home to die — just as it had thwarted Mrs. Nimmo’s request, six months earlier, to have Daisy’s life-support systems removed at home.

“Charlie was in the same intensive care department as Daisy,” said Mrs. Nimmo, a leading advocate for parents of terminally ill children. “It was shocking to see the crazy media circus and these parents stuck in the middle trying to save their child.”

Charlie, who was born with a rare mitochondrial disease that made him blind, deaf and unable to move on his own, died July 28, days before his first birthday; Daisy lived to be 12, racing around in a wheelchair with flashing lights, appreciating nail glitter and slapstick comedy. And while Charlie’s parents engaged in a painful and protracted legal battle to try to keep him alive, Daisy’s mother said she eventually realized her greatest achievement would be to give the girl a “good death.”

“I had a longer journey and I came to accept Daisy’s diagnoses,” Mrs. Nimmo said. “I sometimes disagreed with the doctors, but there was never a complete breakdown in communication as happened with the Gards.”

Experts say that cases like Charlie Gard’s are rare, and that most parents of chronically ill children and the doctors who treat them reach consensus about when and how to end treatment. Cafcass, an independent body that represents children in court cases in England, counted 18 instances last year of disputes between doctors and parents it was involved with that ended up in court.

Another dispute is emerging. A group calling itself Charlie’s Army has begun mobilizing on behalf of the family of a profoundly ill 14-month-old boy in Liverpool, Alfie Evans. Alfie, whose diagnosis remains unclear, has been in a coma since December, and his parents are fighting the hospital’s desire to take him off life support; as in the Gard case, several American hospitals have offered to help.

Alfie’s father, Thomas Evans, argues that Alfie has shown signs of improvement and that it is his parental duty to do everything possible to save his son’s life.

“We do not want to let him die when there could be something to help him,” he wrote on a crowdfunding site where he is raising money for his treatment.

But Dominic Wilkinson, a neonatologist and professor of medical ethics at Oxford University, said that doctors and hospitals sometimes needed to override parental wishes. “Parents shouldn’t be allowed to make decisions that carry a significant risk of serious harm to a child,” he said, for example refusing treatment or demanding treatments without obvious benefit.

Mrs. Nimmo, who lives in Wimbledon, a southwest London neighborhood, worked in marketing and already had three children — two with autism — when Daisy was born, two months premature, in 2005. She was told that the odds of being born with the disease were one in 1.25 million, and that Daisy might not live to her first birthday.

“When your child has such a rare disease, you realize, this isn’t the child I was expecting and you mourn, but you start to love the new child,” Mrs. Nimmo said. “Then you are told your child will be taken away, and then you have to get your head around that. It is an emotional roller coaster.”

Daisy’s condition worsened after she turned 3. Mrs. Nimmo and her husband, Andy, traveled twice to the United States, to Portland and Seattle, where world experts who were studying the same genetic mutation afflicting Daisy met to discuss their research; their treatment had not yet been tested on mice.

“We were initially very excited, until we realized it could take up to 10 years before the treatment could be clinically applied,” Mrs. Nimmo said. “As in the Gard case, we were determined to help her, but I did not want my child to be a guinea pig.”

(In Charlie’s case, a neurologist at Columbia University Medical Center in New York offered him nucleoside therapy, which had been tested only on mice and on 18 people with a different genetic mutation.)

Sacha Langton-Gilks, a music teacher whose son David died from a brain tumor in August 2012, said accepting that there was no cure was the hardest challenge.

She had been determined to find a cure for David’s tumor, medulloblastoma, after he was diagnosed in 2007. But after two relapses, 11 brain operations, years of chemotherapy, a stem-cell transplant, and experimental treatment that had burned through David’s esophagus, Ms. Langton-Gilks said, she decided to focus on giving her son, who was 16, a happy end of life and send-off.

“Like Charlie’s parents, I initially thought it was my right as a parent to decide on treatment for my child: I thought, ‘How dare they tell me what to do!,’” she said.

“The level of pressure you are under as a parent is hard to describe,” she continued. “You can’t give up hope when hope is only defined as cure. But you have to redefine hope as something else when there is no cure. You have to accept that your child will die to give him or her a good death, to stop the suffering and strive for quality of life over life at all costs.”

David spent his final days at home, where she organized parties with his friends and he played with owls, his favorite animal, which Ms. Langton-Gilks allowed to fly in her kitchen. He became a Buddhist, meditated and wrote a will, giving his banjo to a family friend, a tray of jelly beans to his sister and a ceremonial Chinese sword to his brother.

Daisy, too, spent years fighting her disease, with 50 surgical procedures in her short life. She also had to endure the death of her father, from bowel cancer, a week after her 11th birthday. Not long afterward, Daisy’s conditioned worsened and she went into septic shock and cardiac arrest, her mother said.

After she was put on life support, Mrs. Nimmo said she decided it was time to let her go.

“As a parent, the decision to take your child off of life support is the most selfless thing you can do because you want your child to live,” she said. “But you have to ask, ‘Who am I doing this for?’”

As Charlie’s parents would months later, Mrs. Nimmo asked Great Ormond Street Hospital if she could take Daisy home while on the life-support machines, so her final moments would not be in an institutional setting. The hospital refused, saying Daisy might die in the ambulance or have potentially harmful complications that could be handled only by an intensive care team at a hospital, a risk her mother did not want to take.

“The most important thing is that Daisy knew I was there and she knew she was loved and surrounded by love,” Mrs. Nimmo said.

Afterward, Mrs. Nimmo said, she took Daisy’s body home and lay it on a hospice bed. Her sister, Xanthe, painted Daisy’s nails and her brothers, Theo and Jules, sat at her bedside. They played her favorite Disney song, “Let It Go,” from the film “Frozen.”

Mrs. Nimmo, after the loss of husband and daughter in a little more than a year, organizes what she calls “death cafes,” bringing people together to talk about dying. She also writes a blog about a suburban mother whose life was suddenly upended by lethal family illnesses. She credits her three surviving children, along with her passion for jogging and swimming, for her resilience.

“My family went from six to four,” she noted. “ We are open and determined to get on with our lives. That is what Daisy taught us: Make the most of your finite time.”