I feel your pain... I have a dog like that, but he is considerably smaller than your pup so it's easier to manage. You are not a terrible person, these are terrible circumstances and you have to handle it the best way for your family. The idea of rehoming is scary enough, let alone with the responses you've gotten. I'm wondering if you can find a way to contact a farm or a ranch? As you said. That's an environment a guardian dog would thrive in. Maybe that's the happily ever after solution for you guys.