Does the tree look like it is in trouble? When was it planted? If it is ailing, chances are that the dog peeing on it isn't the problem.
How much water does the tree get, how often, and can you tell us about how the tree was planted? The most common problem for ornamental trees planted in people's yards is that they're planted too deep. If the trunk flare isn't exposed to the air it the tree is compromised.
Take a look at the sample photos on this page
If you have a digital camera please post photos of the yard and tree. If you can't make a photo small enough to load here you might want to host it at someplace like Flickr or Photobucket and paste in the link.