Bingowings said:
Ben : The Emperor knew, as I did. If Anakin were to have any offspring, they would be a threat to him. That is the reason why your sister remains safely anonymous.
That would seem to imply there is something special about Luke and Leia and their connection to their father that worries the Emperor but interests Ben and Vader.
The only real connection they have this point is blood.
The look of horror on Leia's face when she discovers Luke is Vader's son doesn't make it seem that affection for her absentee father is a threat Vader or Ben can use against Palpatine.
Though ironically Anakin's latent affection for his child is what defeats Vader and his Emperor.
You have crushed your own argument. The threat that Emperor was afraid of was the very same thing that ended his life in the end. That is Luke triggering something good in Vader that eventually led to return of Anakin.