(CBS/AP) SAN DIEGO -A spokesperson for the DiMaggio family is saying that suspected kidnapper James Lee DiMaggio's sister has DNA samples of her brother and would like to test them with his kidnap victim Hannah Anderson and her eight-year old brother Ethan, whom DiMaggio killed.
The family suspects that DiMaggio may have had a physical relationship with Christina Anderson, who DiMaggio also killed, and that her children may be his and not Brett Anderson's, reports CBS station KCBS in Los Angeles.
DiMaggio's sister was removed as a beneficiary of his life insurance in 2011, which was changed to benefit Hannah's paternal grandmother, Bernice.
"He had stayed with Bernice while he was saving up money to get his house, so he trusted Bernice," DiMaggio family spokesman Andrew Spanswick said. "So he believed she was the solid matriarchal figure in the family that was responsible and would take care of the kids if anything happened."
An Amber alert was issued on August 5 after DiMaggio's house was found in flames. The bodies of Christina and Ethan Anderson were found inside the burned out structure.
Hannah was later located in Idaho with DiMaggio, who was shot and killed by FBI agents.
Brent Anderson says speculation about who the real father is is "disgusting". Meanwhile, the DiMaggio family suggests that they are still friends.
"Lora DiMaggio, in fact, called Brett and had a two hour conversation where they shared their mutual grief and loss over all the victims involved," Spanswick said.
(VIDEO: Hannah Anderson, kidnapper caught on border cam)
DiMaggio was like an uncle to the Anderson children and their father's best friend, driving Hannah to gymnastics meets and Ethan to football practice. DiMaggio and Hannah Anderson exchanged about 13 calls just prior to her kidnapping, although the reason wasn't immediately clear. Investigators who searched DiMaggio's home also found letters from Hannah.
Hannah acknowledged being uncomfortable around DiMaggio before the ordeal, saying on a social-media site that he once told her that he was drawn to her. "He said it was more like a family crush like he had feelings as in he wanted nothing bad to happen to me," she wrote on the ask.fm site.
Hannah said she didn't tell her parents because DiMaggio was his father's best friend "and I didn't want to ruin anything between them."
The DiMaggio family is claiming that the talk of paternity tests is about answers, and has nothing to do with money.
Meanwhile, authorities revealed DiMaggio had a 20-hour jump on authorities when he kidnapped Hannah Anderson, and officials discovered he used a timer to set fire to his rural home where the girl's mother and younger brother were found dead, a San Diego County Sheriff's Department spokeswoman said Tuesday.
DiMaggio was spotted on a Border Patrol surveillance camera at 12:10 a.m. Aug. 4, about 20 hours before his home caught fire, said the spokeswoman, Jan Caldwell. He is seen inside his 2013 blue Nissan Versa with 16-year-old Anderson at a westbound highway checkpoint.
Hannah's disappearance - discovered after the fire - triggered a massive search for DiMaggio, 40, that spanned much of the western United States and parts of Canada and Mexico.
The discovery that the fire was set by a timer prompted investigators to warn the public during the manhunt that DiMaggio's car might be rigged with explosives, Caldwell said. As it turns out, the car wasn't rigged.
Investigators who searched DiMaggio's home found an incendiary device, handcuff boxes and "arson wire," according to a search warrant. It also says they discovered letters from Hannah and a handwritten note, without elaborating on the contents.
Search warrants unsealed last week said Hannah was picked up from a cheerleading practice at 4 p.m. on Aug. 4, but Caldwell said the practice was a day earlier.
Firefighters found the body of Christina Anderson, 44, when they extinguished flames at DiMaggio's home in Boulevard, a tiny town about 65 miles east of San Diego on the U.S.-Mexico border. A search warrant says she was found near a crowbar and what appeared to be blood next to her head.
(VIDEO: Hannah Anderson makes first public appearance)
The San Diego County Medical Examiner's Office said she died of a blunt head injury, without elaborating on the nature of the wound or the circumstances of her death in a posting to its website. The manner of death is listed as homicide.
Investigators found 8-year-old Ethan Anderson's body as they sifted through rubble. Authorities identified his remains several days later by extracting DNA from his bone marrow.
The medical examiner's office said Tuesday that the cause and manner of the boy's death remained under investigation.
Hannah Anderson says she didn't learn her mother and brother died until after she was rescued. She said on a social media site last week that she was "on the road to Idaho" when the fire ignited.
"He had set to wear (sic) it would catch on fire at a certain time," she wrote.
A memorial service is scheduled Saturday for the mother and son in Santee, an east San Diego suburb.