I've avoided this topic until now, but I do want to comment on the mongrel issue. As Sally has pointed out, mongrels are very different to crossbred dogs. The classic mongrel is the black and tan 'Heinz 57 varieties' mutt. We had one from the cat and dog rescue in Edinburgh (Seafield). She was the most wonderful, loyal, devoted, well behaved and beloved dog, strong and healthy. As we took her away from the rescue, someone on his way in said 'ah you've got a lappit-eared worrier there', and so she was - just always wanting to do the right thing. Not a tiny dog certainly but not large either.
On the other hand, crosses of pure breeds can sometimes be disastrous. We took over the care of sisters from a litter of Wolfhound cross Anatolian Karabash pups - huge dogs. As they grew it became apparent that they had totally different characters, one very laid back, the other too intelligent for her own good, but both wonderful, loving, companion animals. They had plenty of hybrid vigour, being strong and healthy. One evening, the bright one ran off, (followed by her sister who was always determined to stop any badness be it a fight between chickens, sheep or dogs) She got amongst our neighbour's pregnant ewes, chased them a long way then attacked 3 of them. Of course she had to be put down, not just for that but she frequently attacked our other dogs, with her sister always trying to pull her off. She would not have been safe being rehomed, as her character was totally unpredictable, so she could have been a danger to children and adults too. It was our responsibility to make the decision but it was so sad. We felt that although in her sister the cross was brilliant and we had a laidback, gentle flock protector, with this lass something just was not connected properly. There had been 11 pups in the original litter and I worried about what had happened with the others.
What I am trying to say I think is that no dog is automatically perfect, whether the breed is famed for it or otherwise, so choose your mum's dog very very carefully, not just for what type you buy but for the nature of the individual animal. Also, she needs to be there to choose her own pet as it may respond differently to her than to you.
We have never bred dogs so I can offer no opinion on that one.