No, they are scheming of their own accord, but the idiot head of the Taira doesn't seem to care that there is a good chance his son will just up and die.
I have to say that this chapter feels a lot more competent than others. It has a clear goal and accomplishes it well enough. In a single word, this chapter is "tight".
It reminds me of Overlord. Clueless leader with powerful subordinates carrying out black ops and dealing with enemies that consider the leader a massive threat.
I guess a PSA for all the illiterate gibbons in here is in order:
This manga is NOT by the author of Horimiya, it's by the artist.
The person who created this DID NOT create Horimiya, only adapted it.
When Victoria has her downfall, she screams about being the only heir to the Kingdom, and Raoul tells her that the King has secret children with concubines. This chapter says that the three children he had before regaining his youth are the oldest ones.
I think that's the most "explicit" the imaginary men have been so far. If I recall correctly, none of them talked about getting them pregnant before, or about "giving them seed".