What if the second girl to appear was the fake one ? They may have sent the true daughter  first then sent the false one (another spy).
This way, the duke would get rid of his own daughter and he would have no doubt that the spy was his true daughter. It's a way to implant a spy and let the duke think that he truly found his daughter.
And in this time line, they didn't find the true daughter in the orphanage where she was supposed to be because she never wa there in the first place. 
I don't know if what I wrote is clear, english is not my first language.