I don't think you fully understand. So what if you got a recording such as you describe? It wouldn't change anything.
1.) It doesn't matter whether or not you agreed to work out of town at the time you were hired or not. Your employer needs you to work out of town NOW, and unless you have a legally binding and enforceable contract that says you CANNOT be required to work out of town, you can.
2.) You can legally be fired for refusing to go work out of town, regardless of your reasons for refusing, unless your reason is one that is legally protected under the law and off the top of my head, I can't think of any that would fit the situation you describe. You may or may not get unemployment based on how it is presented and exactly how the situation plays out, but the termination will be legal either way.
3.) If you can work it out with the employer so that you don't have to go out of town, so much the better. But that is going to be between you and him. There is no law you can invoke that will force him to let you stay in town. If he wants to require you to work out of town, he can. The best you could hope for if he is not willing to retract the request, is UI. And that's not a guarantee.
Two things I am tired of typing: 1.) A wrongful termination does not mean that you were fired for something you didn't do; it means that you were fired for a reason prohibited by law. 2.) The above answer, whatever it is, assumes that no legally binding contract or CBA expressly says otherwise. If it does, the terms of the contract apply.