Dalmatians were on her insurer's "dangerous dogs" list.
Dog bites cost insurance companies more than $300 million a year. So some have decided to ban certain breeds, including Dalmatians. But Daley's Dalmatians are also trained therapy dogs, reports CBS News Correspondent Richard Schlesinger.
"They said it doesn't matter what they've done," Daley said. "They are a Dalmatian and they will not be insured or I won't be insured."
Animal lovers have coined a term for the insurance company's actions. They call it breed discrimination - arbitrarily punishing all dogs of certain breeds because some are vicious.
Carter Luke of the Massachusetts Society for the Prevention of Cruelty to Animals doesn't believe specific breeds, even pit bulls, are violent by nature.
"If we think about the importance of how an animal is raised and the animal's history and the behavior of the pet owner, those are the best ways of determining if animal is going to be a problem," Luke said.
Diane Daley eventually got insurance. It was more expensive but she kept her dogs and her house.
Ten-year-old Alicia Muzarol and her family were not so lucky. They had to give up Sheena, the German Shepherd they had lived with and loved for four years.
"She never bit anybody," Alicia said.
The Muzarols had to choose between their dog and their apartment. The management of their public housing project outside Boston started enforcing a ban on all dogs over 20 pounds.
"This is a place for children, it's not a place for pets," said Michael McLaughlin, executive director of the Chelsea Housing Authority.
"The issue here is we have people whose health and safety and the health and safety of their children are put at risk," He said.
So Sheena had to go. And Alicia still cries for Sheena to this day.