"He would have been the first one not to go," said Cheryl Cooksey, the mother of Andrew Speaker's new wife, Sarah.
The four appeared in an interview that aired Monday on ABC television's "Good Morning America."
Speaker's father, Ted, said he taped a meeting in which a doctor says three times that his son was not contagious. He said he will release the tape at some point.
"We're in hell and we want to get out of hell," Ted Speaker said in the interview.
Speaker, 31, is now receiving treatment at a Denver hospital.
Before Speaker left last month for Europe for his wedding and honeymoon, he said he was advised by Fulton County, Georgia, health authorities that he was not contagious or a danger to anyone. Officials told him they would prefer he did not fly, but no one ordered him not to, he said.
Speaker was in Europe when he learned tests showed he had not just TB, but an extremely drug-resistant strain known as XDR.
A federal quarantine order had been issued for Speaker because he ignored earlier request not to travel, taking a trans-Atlantic flight from Europe to Canada in what he has said was an attempt to return to the U.S. for treatment.
Since Speaker, an Atlanta lawyer, has been isolated in a special room at the National Jewish Medical and Research Center in Denver, federal health officials lifted their quarantine order Saturday night, but it was replaced with a Denver health agency's restriction.