if i were the father i will not stop just because the princess aske me to do. that red haired brat actually just do the Lèse-majesté. for being ruthless he pardoned him is uncanny. he is aware that almost all the noble have some opinion towards his beloved princess. so its bizzare for him not to set an example for them all.
at most i will put the son in the dungeon, strip their family from their title (considering their family is not a duke household or have any royalty lineage because the king casually ordered them to die) and put them in a place where the utmost loyal supporter of king watche them to cut any thoughts about rebellion.
If he is the king as the rumor say, I won't stop just because the princess begged, eventhough adorable and sweet kinda stupid, the princess still a subject to the king so???
and severing the princess from nobility is kinda stupid? she needs supporter especially since the king does not have any sons, so she will be the next monarch, she will need a loyal college and followers. at most i will sever/minimise the other princess relationship and let the adored princess became the spotlight of the nobility.
and why im thinking this too much again? ah probably because that red haired fucking brat tried to be deus ex machina and hero to the otber princess, and failed hard and became an idiot/laughing stock like he truly is. stupid nobility will bring down the country, should've weed them out to let the bright one rises.