Martha Stewart Is a Grandma!
updated 03/11/2011 AT 03:05 PM EST
•originally published 03/11/2011 AT 06:30 AM EST
The baby girl, Jude, was born via gestational carrier on Tuesday.
Though the entertaining guru is surely glad to have a granddaughter, don't expect her to be a typical grandmother. "Martha is going to be called, 'Martha,'" Alexis announced on her radio show, Whatever with Alexis & Jennifer. "She seemed to have no problem with it. ... I was like, 'Do you really want to be 'grandma'? I don't like the term grandma!"
For the past few years, Alexis Stewart, 45, has been open about her struggle to conceive a child, telling PEOPLE in 2007 that she was spending more than $20,000 each month on fertility treatments.
"Having my own kid is the most important thing in my life," she said at the time. "I'm trying everything I can."
Equally eager for an addition to the family was Martha, whom Alexis said has wasted no time spoiling her granddaughter.
"She was born at 1 in the morning ... and [Martha] brings this huge box from Bergdorf [Goodman]," Alexis said. "I open it up and I look inside and it's full of baby clothes, all with embroidery, and I'm like, 'Wow, I guess I'm going to be allowed to buy myself something pretty nice because all this stuff's going back!'
"If the kid can't see it, why the 100 dollar [clothes]?" she continued. "Only books, child appropriate or whatever: that's the only thing that I want. No toys please!"
As for the baby's measurements, Alexis quipped, "You're not getting her weight and length. It's rude!"
Grandma herself shared her excitement on Friday's The Martha Stewart Show. "They're home in New York in their apartment and I stopped in last night after a business trip and I got to see her when she was about 36-hours old," Stewart said. "She is very alert and doesn't cry – ideal baby!"