“Yes, my daughter,” Mr. Parker responded, offering his hand. The man ignored it, and instead spewed obscenities at him, Mr. Parker said.

The man trailed him, “jabbering in my ear,” Mr. Parker recalled in an interview, as he walked for blocks, trying to put distance between the harasser and his family.

“It was absolute venom,” said Mr. Parker, who is a plaintiff in one of three defamation suits against Mr. Jones. “He was absolutely disgusted with the person that he believed that I was.”

Mr. Jones did not respond to requests for comment. His lawyer, Marc Randazza, acknowledged the series of decisions in favor of the families, but said, “If you’re keeping score here, this is just the coin toss.”

Mr. Jones’s role in spreading baseless conspiracies about the families began within days of the shooting.

The night after the shooting, Mr. Parker had agreed to meet a news crew in front of a Newtown church to share a statement about Emilie. Surprised to find a sea of waiting reporters and cameras, he gasped out a nervous laugh before stepping forward to speak.

“This world is a better place because she has been in it,” he said, his voice cracking.

The footage ricocheted among conspiracy theorists, and Mr. Jones seized on it. “He’s laughing, and then he goes over and starts basically breaking down and crying,” Mr. Jones told his followers, according to court documents. “This needs to be investigated. They’re clearly using this to go after our guns.”