
To be honest if your mother is looking to add another puppy it would be much easier and alot cheaper for her to buy one. Breeding carries risks for the mother and can become expensive for the breeder. If your mother is determined to breed she will need to know how everything works, what can go wrong at each stage, what do to if it does go wrong, have the time to be with mother and pups 24h s for weeks and have the money to cover all supplies and out of hours vet bills increase something like a midnight c section is needed.
Normally I would say your best place to ask is your girls breeder but as you said before they don't register their litters unless it's for a friend for breeding/showing that would be a red flag for me. Your mother would first need to get her girl fully health tested, kc recommends eye testing (including Gonioscopy) and DNA for pra. I'm surprised they don't include hip scoring it'd look into that too.
As your mother's girl is not kc registered she may find it harder to find a responsible stud owner who will allow their boy to be used, whoever you use make sure he is fully health tested too. You could try contacting your breeds club see if they keep a stud list or recommend someone.