The most important thing for you to know is that you need to take your documents to a lawyer for proper advice. You will not fare well trying to handle this on your own relying on freebie comments from Avvo.
You face an uphill battle on the arbitration issue. A lawyer looking at your documents may see something that gives you a way out of arbitration, but it is not likely. If you sign an agreement saying you will arbitrate your disputes, a court will probably enforce it.
If you have agreed to arbitrate, the builder could open an arbitration proceeding against you on his own after receiving your demand. That would be very unusual, but it is possible. Again, you need to have a lawyer actually review what the builder sent to you to determine where things actually stand right now.
There are few things in the law that are certainties, but it is a near certainty that a city in the state of Washington will not be liable to anyone merely for granting a permit. It is hard to believe that the city gave the builder a permit to do what you are describing. If you haven't done so already, you might consider complaining to the city to see if there is something they can do about this problem though permit or code enforcement.
On the ultimate question of who is responsible to fix this problem, you will definitely need to hire a lawyer to sort this out for you. The builder might be liable, but the contract that you signed with the builder might let the builder off the hook. There are unscrupulous builders in the state of Washington, and, unfortunately, the law in this state is extremely favorable to home builders in terms of enforcing onerous contract terms that they slip into their contracts with unsuspecting buyers.
Although this may be unpleasant for you to consider, your best route from a legal perspective may be to go after your neighbor. Even though your neighbor didn't cause the problem and presumably wasn't aware of it when they bought the property, the fact is that they now own the property that is the source of the problem. So your neighbor is probably on the hook regardless of what happens with the builder.
Take the papers to an attorney, the builder can not force the city or other parties into arbitration. Let a court decide.
My name is Stephen R. Cohen and have practiced since 1974. I practice in Los Angeles and Orange County, CA. These answers do not create an attorney client relationship. My answers may offend I believe in telling the truth, I use common sense as well as the law. Other state's laws may differ.. There are a lot of really good attorneys on this site, I will do limited appearances which are preparation of court documents it is , less expensive. However generally I believe an attorney is better than none, but many will offer a free consultation and a face to face meeting generally will be better, I like my clients to write a short one page history of the fact and questions they have prior to meeting with them, so nothing is forgotten.