I'm not sure what information is being withheld, did I forget to mention the dog breed? He is half corgi half shelti (sp) I was not present so I can only tell you what I have been told.
People have been asking since page 1 what kind of dog it is and what the circumstances of the bite were because it does make a difference in understanding what happened.
That information right there says a lot. Being derived from two strong herding breeds, the dog has strong herding and protective instincts, especially with children.
We humans have been breeding herding dogs for thousands of years to do what they do best, and the way they do it is by (warning) barking and nipping moving animals to "keep them in line". Animals instinctually understand what the dog is "saying" to them and therefore they comply; children usually do not.
Two of the three bites I've had in my life were from two different Shelties (Shetland Sheepdogs) when I was a child. They can be very nippy if not taught how to behave by an owner that's a strong leader.
Owning a herding breed, especially when there are children around, comes with certain obligations, and those include keeping people who visit your home safe from a dog who is thinking a certain way about them. In other words, there is always the potential for a bite because herders are doing what they instinctually do. Having German Shepherd Dogs, I live with this daily as well.
Dogs need to be taught to look to their owner for leadership in situations. That leader will signal "There is nothing wrong here and you can relax, I've got it under control". Admittedly, this takes a long time to achieve via training and successful experiences. If there is no leadership, then you have a dog who's going to do his own thing, and as we all know, dogs who do their own thing can be dangerous to people.
It sounds as if this dog has had no or poor leadership and inconsistent training, if any. So naturally it's no suprise there are repeated problems.
The problems for the dog started when he was aquired by someone who didn't understand the breeds he or she was getting involved with. Then little to no training. Then passed off when problems occurred. And now his very life hangs in balance because of the mistakes his people have made. Sadly, there are many dogs who've suffered the same fate and as much as people try to educate others, only some get the message. These are the fortunate ones.
We would never, I'm sure, be able to agree on whether this dog deserves euthanization or not. Some people do euthanize dogs like this because they consider it a kindness rather than passing the dog around and around, only to have things happen again. The truly sad part is that in the right hands and home, he'd probably be fine; maybe he'd even make a great working dog. But the reality is, is that that home is going to be elusive. And because of his history, he should be kept away from children.
I'm going to keep my comments just to the dog, others can advise on the family situation. If MIL keeps the dog and you bring your DD over there, the dog needs to be put away in a different area of the house, fully secured, before your DD goes in the house. If it were my child I'd be checking on it as well to be sure it's secure.
I have some additional thoughts on your DD and dogs, but I have to run out, will post later.