How distressing for all involved, but moreso your mum. She hasn't lost her dog, or pet, she's lost a true loving friend. A companion. A furry child-compensate. My heart aches for her loss.
I myself come from, and continue to live within a family that cherishes animals. They are one of us, and deserve the same rights and care. You don't just 'accidently strangle a human'. I know that is VERY OTT, but it was sadly avoidable. I'm not insinuating that there is any malicious intent, but more a lack of true animal professionalism and care.
If I was in this situation, I would seek all financial compensation possible (vet bills), report the actions of this business owner to the RSPCA and to the ombudsman (or whoever will make sure these people do the right thing in future or don't practise at all.)

Sincere and heartfelt condolences over this tragic loss.
xx