Unless "Lady Mendelson" is Georgiana Darcy then it can't be Elizabeth and Darcy and if she is Georgiana Darcy then this makes no sense within the reading of the book, also a title cannot (even today) be passed on to an illegitimate child and at the time the land which went with the title also couldn't go out of the legitimate line..it would have gone to the nearest legitimate male heir (as also made clear in the book!)

This was too full of holes for me I'm afraid, I rarely read fan fiction based on novels and this has only confirmed my reluctance.