So last night...

You're pretty nice I think. Easily just coulda let your dogs kill it and tell the neighbor to clean up the carcass. Or pulled your dogs off and given em five minutes to get their goat off your land. And building your fence back and losing a foot of land? Much more than I would do.

Sounds like your neighbor is half reasonable though. Understanding the goat and their fence was at fault. Not you or your dogs. Nothing worse than someone who can't take personal responsibility for a damn thing they or their property does. Hope it works out for the best and they build a proper fence.