I don't think the MyTwinn dolls have the same cord- they were made a little differently, much more custom- the dolls were made from a photo of the child. Facial features like freckles, moles, dimples, even scars. Face shape and of course, hair color, length and style. They were eerily like the child- kinda creepy, actually.
Later, MyTwinn was bought by another company, and though the dolls were still customized, they were not exact replicas of the photo. I don't know which version Patsy ordered. JB also had a few of the American Girl dolls, which are actually play dolls. The MyTwinn was meant to be more of a keepsake doll. IMO, Patsy wanted to keep a memento of JB at her pageant best. Kinda freeze her at that point in time- it was really a doll for Patsy. In a way, that was accomplished with JB's death. She'd never grow old. Or grow up.
JB was not impresses with the doll that Christmas morning- she tossed it aside saying that it didn't look like her. Patsy must have been furious- that doll cost a lot of $$$ and she expected JB to be as thrilled with it as she was. It was probably the first of the Christmas Day altercations between PR and JB.