Should I go arbitration or Court to solve dispute?

Arbitration is by agreement.  If the contract provides for mandatory arbitration, you would be required to arbitrate unless the other party or parties agreed to go to Court.  Conversely, if the agreement did not require arbitration, you couldn't arbitrate unless the other party or parties agreed to arbitrate.  Usually an agreement to arbitrate would have to be explicit; I have my doubts whether an agreement which provides that disputes shall be resolved in the usual manner would be enough to allow you to compel another party to arbitrate.  If you go to Court, the Court will apply the proper law to resolving the dispute (probably the law of Wyoming, uless there is some jurisdiction whose law is more properly applied), not rules of arbitration.  You can have an agreement with a choice of law provision (i.e. "this agreement shall be construed in accordance with the law of the State of New York"), and usually such clauses are enforceable, but you don't say that there is such a clause in the agreement. Also, although I am not specifically familiar with the arbitration "law" to which you refer, I doubt very much that it contains any substantive "law".  Arbitration rules usually deal with procedure (i.e. the respondent shall have 30 days to respond to the claimant's claim, no discovery will be allowed, there will be a panel of 3 arbitrators, each party will pick one and the 2 picked with choose the third, etc.) not the substantive law (e.g. whether an agreement has to be in writing, how a contract is to be construed, etc.)  Arbitrators normally try to apply the same law as a Court would.  As for procedural rules, a Court will apply its own rules of procedure to any dispute, not the rules of any arbitration association.