B., So great that you are concerned for your MIL feelings about this.
Our society recently has made it very difficult sometimes to make the right decision regarding our pets. The boost of rescue groups & the "adopt a pet, save a life" campaigns have people believing that -every- dog must be saved, regardless of circumstances.
Facebook & other social media have made this even crazier - I have seen postings for dogs that have mauled children, and there are people commenting that the dogs should not be put down, but rehabilitated instead.
So when someone like your MIL makes a decision that is heartbreaking to begin with, but knows it is the right decision for her family, the dog, and anyone that might have been at risk, it becomes a very emotional issue. She knows she did the right thing, but to say so out loud is going to risk vilification, and possibly judgement from people who may think she took the "easy" way out & "cost a dog it's life".
Dana K. below has the exact response I would suggest giving. It acknowledges that regardless of the circumstances & the actual action taken (what you know happened, or what she may say instead), it was difficult for her & you are sorry for the hurt she is experiencing.
I hope the conversation (if it takes place) goes well. T. =-)