If there is a divorce case and through the process of declaring a
parties financial position it comes out that one of the parties has
dodged a bit of tax can that evidence be held against them?
Generally speaking yes, unless the relevant prosecutor's office provides a grant of immunity from prosecution for the matters disclosed, which basically never happens in a divorce case or ordinary civil case. This is why it is sometimes necessary to invoke the 5th Amendment in the context of a civil case.
Does a judge have the duty to report any law-breaking that arises in
No. It isn't improper for a judge to report law-breaking that is observed in the course of litigation before that judge, but the judge has no duty to do so (absent some very specialized exceptions like treason), and, in practice, rarely does report law-breaking not directly before the judge to evaluate.
In contrast, in criminal cases, during the pre-trial phase of a case (and especially in the pre-arrest phase of a case), a judge often has a duty to keep knowledge of crimes obtained in that way secret until it is disclosed by the prosecution (unless the prosecution improperly fails to disclose something that it is required to disclose). This is so that criminals aren't "tipped off" by a judge of an impending arrest. A judge in Colorado was recently prosecuted and removed from the bench for a disclosure of that kind.
or is a civil case confidential between the two parties?
A judge can seal a civil case, or limit public access to certain documents, but that is the exception and not the norm and has to overcome constitutional protections of the public's right to public trials that media organizations frequently enforce successfully. Confidentiality between the parties can only be imposed for "good cause." Hiding the fact that you cheated on your taxes from tax collection agencies does not constitute good cause.
Most U.S. jurisdictions have an ethical rule for lawyers that prohibits them from threatening to take administrative or criminal actions to gain advantage in a civil case, although the exact details vary quite a bit from jurisdiction to jurisdiction. This does not apply to clients of lawyers acting unilaterally and without guidance from their lawyers.