Thanks for the translation!
As I thought, she's making for a great empress already. Isn't taking any shit from the nobles, but not coming down unreasonably hard either. Though it's hard to say that from the five seconds she's been in power. Hopefully she can handle the Duke as smoothly.
The whole deal with the duke is kinda messed up. His son realizes that his father's mind is totally gone, and he may well already be dead. Pretty messed up thing to figure out about your family, no matter how estranged you are.