I don't really have any concrete answers but I sure as heck wouldn't keep my mouth shut and let one of my kids get bitten. That sure isn't going to help the family dynamic. The first thing I would do is remove my kids from the situation, however you have to do that.
I would definitely not introduce another dynamic into the already complicated situation by bringing my dog.
If this is SIL, I might have a talk with my bro. Tough case but let me share a little story.....
My uncle had a K9. Dog was old and my uncle being selfish refused to put the dog down. My father had been on him for quite a while to put the dog down to the point that it was causing issues in the family. One day I walked up beside the dog and next thing I remember is waking up in the hospital, 52 stitches in my neck where the dog had attacked me. I was 6 or 7 years old. This situation did not turn out well for me, the dog, or my father/uncle's relationship.
My point is, if something happens it will be worse than a little friction. However, it is definitely a touchy situation.