The mom is certain the empress will not bare a child because the issue is within the “emperor”, so won’t her plan backfire once the cousin marries “him” and the outsiders from the court notice she also can’t bare a child? Or does she seriously plan on getting the girl pregnant by a random dude just for the sake of her having power? It’s very likely.
But the current empress could do the same — much to us GL fans dislike, if the story really decided to dwell on this, the more sensible course of action from the “emperor” himself would be to convince “his” wife (that loves him so much and would not be ok with that) that she has to do it unless the whole court will know of “him” being “impotent” or blame her and separate the couple.
I do hope the “emperor” pulls some strings and adopts a young boy to be the successor, it’s not something uncommon, and it wouldn’t be frowned upon if it were a family member. A little cousin or something. The family will still hold the power.
Anyways, ancient politics.
P.S: Ma’am, give up. Your niece wants to marry the female general (?).