You summon the priests of love to the palace for a talk.
In a side chamber, with your wife in ashamed attendance, you question the priests if there's a way out of this that keeps your reputation and allows your wife to pursue her lady-lovin'.
The wise men and women of the clergy discuss this for a while.
"My liege!" Says one of them. "If she were but a lowlyborn, this would be non-issue; or if she were unmarried, this would be non-issue; if she weren't part of a ruling dynasty, which needs heirs, this would be-"
"My friend, but our liege already has a heir. Several, in fact!" Says the priest of family hearth, and the priestess of childbirth nods in agreement: "Aye, our lord and liege has had his family requirements fulfilled by the deceased Queen Milka, and for this there is no doubts." The priests murmur and nod to each other.
"Marriage is sacred, but of course affairs are not unheard or uncommon." Says the priest of matrimony, rubbing his chin. "Divorce! That is the correct choice. That, or your Majesty weathers the gossip of the affair. As your Queen is fancying a woman, there's no dire fear of bastard children by a lesser man, so at least the worst of three infidelities will be avoided, sparing most of the shame." Other priests look at each other or nod their heads, seemingly agreeing with this assessment.
A) "Fine then! Let the rumors run their course, and I will repair that which will be damaged by them."
B) "Fine then! Call for the Advisor, a divorce contract must be written at once!"