TS, I can see why you're mad after reading the thread. It's her dog, she's home all day, she guards her stuff from the dog, but lets it destroy everything else. That's pretty shitty.
Having said that, this is one of the easiest situations in the world man, how would you possibly think about taking your kids and leaving your wife over it??
The dog is a puppy, train it with consistency and it will learn.
Talk to your wife and tell her how you feel. Be honest man. Being honest doesn't mean yelling and screaming either.
They're just material possessions, your relationship with your family is far more important and that dog is a part of your family.
Really seems like other things are playing a part in your frustration.