I still find it funny that this entire thing is basically all because of a potential affair. They are going to such great lengths just to either A) cover it up, B) expose it, C) use it to bring about reform, and/or D) make personal money and status gains. It always is interesting to see people try and cover up/fix a scandal, by making a different scandal which could be said to be even worse.
If you ask me, hiring assassins to kill one of your family's children, just because you suspect her birth is questionable, but lack any actual proof is kind of a shitstorm if it was leaked. For 1, the kid didn't do anything wrong and 2, since it was done without conclusive proof, it brings to question just how stabile is the family, where they would be so afraid of a child that they hire professional assassins to kill her just, because they were suspicious? What else are they paranoid about? Are their other potential things that have been preemptively "handled" without even confirming them? It throws away more or less all of the public trust, which they already seemingly have none of anyways if these group members are anything to go by.
There are way better ways of handling this. Publically force your opinion and exicute them for having an afair, this keeps lets you somewhat save face, and also provides an opportunity to squash possible other interest groups from using this possible "weakness". Since it was done publically, that becomes the truth since even now finding the real truth has been this hard, that even with their best efforts, they couldn't find the answer. Who would still go to the same lengths once the issue had been already handled?
Another option is to simply exile or denounce her status. She was proven to be useless until MC showed up, so why not just change the narrative to saying that even though she was hopelessly powerless, we allowed her to still become an "honorary knight" since her sword skills were still good and she is at least half Angle. That way if she actually becomes proven to be 100% legit, you can welcome her back, and if not, she is just another knight serving you.
Another option would be to have MC fake her death with a double (if they really just had to kill her), and bring her to Jack Raven as a potential recruit. Though this is harder because of all the red tape and that the higher-ups may not accept it, it isn't too bad of an option.
Now I may have overlooked a thing or 2, but honestly, that the main driving point for all of these events happening is just because of a supposed afair still is crazy to think about.