wife says... dogs go or i go:(

Jmo but just from what I've read it kinda sounds like she wants out of the relationship, but doesn't want to be the one to say it. Making you sell your dogs, house, and give up something you love because she doesn't like it seems kind of extreme to me. Sounds like she's trying to push you out. So when someone ask what happened she can put the blame on you. I respect you for wanting to make it work for the kids but she needs to chill out and be willing to compromise some. If you keep giving in to her demands the resentment will keep building up in you until you get to the point where there's no chance of reconciliation between you two.
I agree you guys should check into seeing a counselor, because it definitely sounds like there's bigger problems than the dog getting ahold of the goat. I hope everything works out for the best for you and your family.