Legal Question in Family Law in Utah

The arguments are constitutional. You may want to research what New York has recently done.

In the State of Utah? Nothing. In order to be divorced in the State of Utah, you must first be legally married as that is recognized by this State. The Utah Code specifically defines marriage as being between a man and a woman. Unless you're willing to spend literally hundreds of thousands of dollars in legal fees to work the case through the court system up to and including the United States Supreme Court, there really isn't much you can do. A much cheaper option is to move to a state that recognizes gay marriage and file for divorce there assuming you can meet the requirements to establish that the marriage is valid in the first place.