There was no such thing as investigative journalism back then. Same goes for Facebook. Nobody would have known the king had knobbed his own girl. Rumored, sure, but not enough for any sort of casus beli. So no civil war, unless you want to take the game into absurd territory.
Besides, a few historical kings (real jackasses) insisted their sons weren't 'man enough' and bedded their daughter-in-laws on their wedding night. Hardly anyone protested (certainly not the sons, who just wanted to avoid being killed for 'treason').