Are there widely accepted rules related to union officers being on faculty senate? The faculty senate at my school recently took a position on a professional issue that was highly confrontational toward the administration. After union negotiations resulted in a pay raise, the senate reversed itself on this issue. It was later revealed that the original position had been advocated by the union as a way of applying pressure in contract negotiations. Some but not all members of the faculty senate knew about the union's advocacy of the action. There was no direct or logical connection between the professional matter (the hiring of a vice chancellor) and the contract negotiations. A large number of union officers are also on the senate.

Do other schools have rules or standards of ethical conduct that cover this type of conflict of interest? Is it considered normal for there to be so much overlap between the union leadership and the senate, or for the senate to act so closely in concert with the union as part of labor negotiations?
Many faculty senates agree to be governed by Robert's Rules of Order. Buried in it is this clause:

No member should vote on a question in which he has a direct personal
or pecuniary interest not common to other members of the organization.
For example, if a motion proposes that the organization enter into a
contract with a commercial firm of which a member of the organization
is an officer and from which contract he would derive personal
pecuniary profit, the members should abstain from voting on the
motion.  However, no member can be compelled to refrain from voting in
such circumstances.
Citation: http://www.cityethics.org/content/roberts-rules-has-conflict-interest-rule-local-governments-no-conflict-provisions

Note that it says that members cannot be compelled to abstain and so there was no violation per se. So in your case, I think the best thing to do would either to work within the Senate to all for an inquiry possibly leading to an impeachment or vote of no-confidence in the leadership.
If you want to avoid direct confrontation, you could leak this to the administration which would be happy to do the inquiry for you, but this would be seen as highly uncollegial and quickly make you unpopular.
How about asking the Chronicle of Higher Ed to look into this as a third alternative?
Edits: Clarifications and obfuscations.