@aitak : We don't see his expression in actual the last moment in ch 1 (we only see him next to the bitch, but not his expression)
Him ordering her execution is likely the same as when Keira think she must do X to be proper: He is the duke, and the people demands the 'fake' be executed and he could not find anything to change the situation.
I think his face on ch 5 is the one telling his real feeling in all this.
He thought that even if Cosette looked like the old wife, Keira is his daughter and once her power awaken the truth will be revealed, that's why he thought there was no need to worry.
Then that happened (though I do wonder why didn't Keira also show her power? The chapter implied that she also awakened to the power so if she just revealed hers there would've been room to argue back)
As for why he's silent about it: Reminder that he is her father, and she very much inherited that social skill lv 0 from him...
I think it's a bit ironic that the people call for his suffering are basically acting just like those people calling for Keira's death before.