to which / which /that

I would replace the first to with a comma - or add a comma and get rid of the second use of it.  I also have a problem with the word both here.  In an arbitration situation, you have one arbitrator and two or more parties.  That's at least three people who are subject to the principles.  If you want to make abitrator plural, then you mean all arbitration situations and both isn't appropriate.  If you want to stick with the word both, then keep arbitrator single and be clear that "the parties" is treated as one other entity.  (The arbitrator is also a party to the occasion.)

Common principles of arbitration, which both the arbitrator and the disputing parties are subject to, are enshrined...

Common principles of arbitration, to which all parties are subject, are enshrined...