Yinyang, I am so thrilled for you - some of you might remember that Rover was returned to us after seven months away, he'd been living wild and only went to houses (where he was well received and kindly) as the autumn started to draw in.
I was worried that he wouldn't remember us (and certainly worried that the existing cats would resent his return) but within a couple of days, he'd settled back to sleeping in his old place, etc.
However - this is a different call, your Nibbler's been living with people who sound kind and caring, and she obviously likes it there or she wouldn't have lodged there.
Given that you have the new cat, and you are moving, it might be kinder all round to leave Nibbler where she is. You know she's OK (and I remember that that was the major part of our grieving, not knowing) and the people sound nice. If I were you I think I'd ask if you can be kept informed of her welfare, and keep an interest in her (Rover still sends a Christmas card to the kind family who took him in, and handed him in to the vet). At least you can give them her vet card and other information, so she no longer seems like a wandering stray, but more like a welcomed "adoptee". Take comfort in the fact that she is happy where she is.
I take comfort in your story in that our Rover arrived with us in exactly the way your mum's cat did - he came to a garden where cats lived, looked hopeful, and lived in the shed on top of the boiler for three months before he dared venture into the house (that was nearly ten years ago!) An adopted cat can be exceeding happy in a new home with loving people, even if it's not where he originally started out.