documented as well as possible. Have your wife write down her recollection of everything. If you can, get a statement from the neighbor and the owner.
Take pictures of everything.
Obviously, get it treated (and you frankly might need to get the dog tested for any kind of transmissible diseases). Antibiotics are probably a must (though I'm not a doctor; I'm just a lawyer).
Get in touch with neighbor's homeowners insurance.
Also, a PI attorney would be good to talk with. You don't want to settle with insurance without first consulting one. I have some good connections to firms along the Wasatch front if you'd like to talk to somebody and are in that area--I'm also happy to chat with you two directly just to talk it over.