"It's one hundred percent not true," Maynard tells PEOPLE exclusively of the cheating accusations.
According to reports, the couple had a blowout fight while vacationing with Holm's family and Maynard's 7-year-old daughter Ricki in Myrtle Beach, S.C., last weekend.
"It's funny to me," Holm tells PEOPLE. "We were in a gated community in a private home with just my brothers and sisters. It's just bogus a 'source' would [say] we were fighting. None of that is true."
The report, which claims Holm asked Maynard to pack up and leave the vacation early, made him scoff. "They must have packed me up, too," says Holm, who left the vacation at the same time as Maynard.
The couple are now back in Charlotte, where Holm says he's spent the past two days looking at apartments and condos to move into so he can be closer to his fiancée and her daughter.
After dropping off Ricki (who's now in the first grade) at school together on Wednesday, Maynard and Holm decided to respond to the latest rumors because they were so stunned by the false claims.
"I have never been more in love or felt more confident about our relationship," Maynard says. "We're so excited about the future and to be back in Charlotte and things are actually happening – looking at places to live and going to school. I'm happier than I've ever been."