True but this is also a way to see his allies are loyal to Jin untill the end so what's she doing is good and his father will acknowledge this also he is probably testing his support to now he clearly can see who's loyal to his son and who's not... This also prove that Jin will be the best choice to have the full house run runcandel it's all in Jin favour also it's his plan this whole time... Jin wants to let his father know if he gets to be the one to be the rightfull heir he will bloom his family name with great family alliances with great support by his side thus what she is doing is good! He is not alone and tougher their unstoppable great view for his father too
It's totes to see if those that had allied on Jin's side are true to their alliance or not. It's a test within a test, plus Daddy dearest believes in Jin's ability to overcome any tribulation while also knowing Jin has a place he can run to that no one else would be able to get to or even know how to get to it.

Ice lady, stay away from family issues, just because you want him as a sil doesn't give you the right to get between father/son moments
fuck off lady