Shrien Dewani, 30, is accused of hiring a hitman to murder Anni, 28, on their South African honeymoon.
The young woman was found dead in the back of an abandoned taxi with a bullet wound to her neck last month.
A close family member said he was speaking out to set the record straight.
He dismissed insinuations of a rift between Anni's relatives and his own family, saying: "Everyone in both families is stressed out by these spurious allegations and wants justice.
"There are good relations between the families." Demani, the family member said, is torn apart after losing "the woman of his dreams".
The family spokesman said: "He's distraught and devastated, he's lost weight and is completely shaken. He's completely traumatised, he can't sleep, he can't eat, he keeps getting flashbacks."
South African authorities want to extradite the Bristol care home owner, who was granted bail in the British courts earlier this month.
Although his family would not be drawn on whether they believed he would get a fair trial in South Africa, the spokesman hinted that their faith had been badly dented.
"Comments from people in positions of seniority, power and influence have served to further confuse and diminish the confidence that the family has," he said.
The family rubbished claims he stood to gain from his wife's life insurance policy and was having an affair with a male prostitute.
The family member said: "They dated for 18 months, decided they wanted to marry and arranged their own wedding in India. Shrien wanted to have a family with Anni and plan a future with her."
Taxi driver Zola Tongo, who drove the newlyweds to the dangerous Cape Town township of Gugulethu where his cab was hijacked and Swedish Anni was driven off and killed, claims that Dewani offered him 15,000 rand (1,400) to arrange her death. He made the claim as part of a plea bargaining deal.
"The taxi driver's gain in this is a significant reduction in his sentence," the family spokesman pointed out.