FREEPORT, N.Y. (CBSNewYork) – A Long Island family is fighting to get their beloved dog back, but an animal rescue group is not eager to return the pet.

At Bobbi and the Strays animal shelter in Freeport, she goes by the name Blue. But in Stony Brook, the Osborne family knows the same 5-year-old dog as Luna. They say she is theirs and they miss her.

“I came and the first thing I said was, ‘All her toys are still here, she’s gone,’” Linda Osborne said.

She had to go to an in-patient rehab center after being hospitalized for a diabetic condition. Doctors told her family she may never leave. So her son put her shepherd-beagle mix up for adoption on Craigslist.

“He was cornered. He was worried about me,” she said.

Osborne pulled through, but in the meantime, a man adopted the dog but then decided to get rid of her, dropping her off at a kill shelter without telling the family.

That’s when Bobbi and the Strays rescued her and, by chance, Osborne found her on their website.

“I saw her and I screamed for the boys. They had her as a neutered male, we’re like, ‘no, that’s her, we are going,’” she said.

When they tried to get her back, “she jumped all over us, kissing us.”

That’s Osborne’s story, but shelter volunteers tell it differently.

“It is scared silly of the son,” one volunteer said.

He said the shelter won’t give back the dog, because they feel the family’s home and backyard aren’t fit, and because they gave the dog up for adoption on Craigslist, which is dangerous for pets.

“They feel sorry for the mother. What about the dog?” the volunteer said.

Osborne admits her son should have never put the dog up for adoption in the first place, but had no idea she would end up in a shelter.

“Bad things can happen on Craigslist, but Timmy admits he made a horrible mistake,” she said.

The family now plans to get the authorities involved and take legal action.

Osborne’s adult son even said he would move out if that meant his mom could get her dog, but the shelter still won’t allow it.