Can my employer force me to sign an arbitration agreement with a 3rd party?

I work for a sales and marketing company as a sales representative. My company has a contract with a electronics manufacturer. I work in a store that sell the manufacturers products. I take my day to day directions from an employee of the manufacturer. I do not take direction from any store employee nor do i handle any transactions or inventory in the store. My employer (the sales and marketing company) is requiring me to sign an Arbitration Agreement with the store requiring Arbitration from any claims and not allowing them to bring them in court. This includes common law and torts matters as well. Failure to sign the agreement will result in termination of my employment. Can they fire me if I refuse to sign? Is it binding if I do sign it?