Claims of political support due to their marriage is just not true.
If she can judge, if she can choose- do you really believe that if the circumstance arises where she has an opinion- that the fact that Souma is family, and her king won't tip the scales regarding her decisions/opinions - even a little bit?
Yes, I absolutely believe that she does not let 'family' get in the way of her policy. Not even a little bit.
Castor was her son-in-law, Carla was her daughter. Their siding with Georg's rebellion did not convince her to join him, or even go softer on him; as far as I can tell, it didn't change her policy at all, she was all-in on Souma's side.
The most she did was try to get them a lighter sentence - and that was after the battle, where it didn't matter.