The other side will not be successful in getting the records from the IRS with a state subpoena. It is common for the opposing counsel to get the records directly from the IRS with a signed release. Most likely, the opposition will request you sign a release and file a Motion to Compel if you refuse. If your wages or income are in issue, it is likely the judge will allow the adverse party to get the records.
Generally, tax return information is discoverable if relevant to a proceeding, but not through the IRS directly in the situation you describe (civil matter between private parties). So the other side would need to go through you.
Internal Revenue Code 6103 prohibits disclosure by the IRS except as provided in the statute. You can read about the restrictions at the IRS web site -- http://www.irs.gov/Government-Entities/Federal,-State-&-Local-Governments/Disclosure-Laws
Or see the code section at -- http://www.fourmilab.ch/ustax/www/t26-F-61-B-6103.html
This answer or response should not be considered legal advice, and does not create an attorney-client relationship. If you have further questions, I would be glad to discuss your situation further. I can be reached at US - (801) 746-6300, or online at -- http://www.lewishansen.com/attorneys/robinson.html
Tax returns are often discoverable, but not through federal or state sources. Unless there are unusual circumstances, particularly in a civil proceeding, the returns would be requested from you directly, not 3rd parties.