Hey Scoot,
Ya did the right thing my man. Personally it would have been gone in some fashion after chasing livestock just once. Totally unacceptable behavior in agri land. A canine as big and 'uncontrolled' as yours needed aggressive consistent training by a dedicated owner. Once a dog or cat makes aggressive action towards a child, it's the one strike rule.
I had 18 sled dogs for a 3 year period 24 years ago while I lived in the mountains. When I changed my lifestyle I had to get rid of them all through give aways and put downs. The give aways went to good homes as the dogs were gentle and manageable. The put downs were way too aggressive for family use.
Over the years of my growing up, putting down of old family dogs was just a part of life. Hard to do, but mercy kills are hard to do no matter what.
I feel for ya. Food for thought; Some times telling the truth after a very difficult decision is a good teacher as well.