A motion to recuse based on the allegation that the judge has already made up her mind is a bad idea. If you were an attorney and you were representing a client, this would be something to potentially do. But in your case, where you are pro se, the judge is simply going to get angry at you and deny your motion. The reality of your situation is that because you are representing yourself, the judge will not look favorably on your case. Judge's do not like pro se litigants.
It may not be fair, but it is simply a fact that you have to deal with, as there really is nothing you can do about it (i.e., trying to sue the court for violation of your civil rights
, and trying to do this without a lawyer, will simply take you down a path you cannot win on). I'm being perfectly blunt with you because I don't want you to be misled about your situation.
The mandamus is the same issue, except that the judge does not get to decide on the issue, the appellate court does. Here, you would say that the judge is grossly abusing her discretion and is acting without any reasonable basis in law or in fact in failing to overrule the objection and allowing you the requested discovery.
In all likelihood, the appellate court will simply tell you that they will trust the judge's discretion in this case at this point in the trial, and that you can simply wait for the end of the trial to appeal the matter if the point is not moot.