I would have done the same.

You need to protect the family, including pets and act with the same force you face.

I feel strongly also about teaching the kids that violence is part of nature and we don't live in a bubble. They need to understand it, so others who also do and want to prey on them with it are less able to.

We are pretty open with death also, on their level. When they saw how our dog killed a mouse we discussed it. Why it happened, how it happened, and why it is ok, and when it would not be.

Actually your described situation, when animals fight, is why we bought now a standard (large) poodle. It won't pick a fight but with it's height and ~kg weight it can survive and handle most animal attacks without the kids need to interfere. I really wanted a stafford again, but my four year old girls charming, giggling, bubbly voice is not enough in a situation to call back when it thinks it protects the family. In a few years she could also handle that if we raise her right.

Go daddy, this is the way!