Joan Lunden and family
Courtesy Lindsay Krauss Weinberg
09/05/2014 AT 08:45 AM EDT
's family just got a little bit larger!
The former Good Morning America
host's daughter Lindsay Krauss Weinberg welcomed baby girl Parker Leigh on Aug. 30.
"Everything is wonderful and this has been the most amazing experience ever," Weinberg tells PEOPLE.
"Part of what has made it so incredible is that we're experiencing it with our families right by our side! My mom was literally with me at the hospital even though I know she didn't feel well at 1 a.m. as I was in labor," she adds. "She came right back at 6 a.m. when Parker was born! It was truly the most special experience ever."
Lunden has been battling triple negative breast cancer
, a rare and aggressive form of the disease, since being diagnosed in June.
"When something like this happens, you learn just how important it is to have a support system," she said during an interview with Robin Roberts
, where she spent 17 years as an anchor.
Though Lunden is overjoyed about the new addition to the family, when it comes to her new title as "grandma," she's considering a twist on the tradition.
"I'm like Marie Osmond in that commercial where she says 'Grandma? I'm not old enough to be a be a grandma,' " she jokes. "Then at the end she says 'I'm a Glam-ma.' I can handle that, Glam-ma."