Eh, I don't really agree with this method either but it is what it is, civilians can't stand up to the army of a tyrant after all, and fear is a very effective control tool, people can do really messed up things just to get by for one more day. Rebellions can be squashed with brute strength and she has the support of a faction of the nobility so it's not like she is isolated. The puppet king would be more useful for diplomatic stability instead of domestic affairs, that much I can agree on.I don't really agree with how civilian lovingg you or not doesn't matter. They are your most precious resource: They feed you, they feed your armies and you know, they are your 'armies'. If you are marked as usurper and if you are the one who broke the peace then you must surely get ready to be antogonized by them. Oh, and also don't miss the part that Cass known for her sinister and wrathful nature and well... she is a woman. Not a good combination. Also, If it's known that you are the head of the coup, marrying somone wont change a thing in the terms of popularity. Even them civilians can notice what puppet king is XD.
For Conrad part: I dont really remember whether Cass talked about Conrad or not. But her plan -atleast 1st plan- is not going gun blazing but blackmailing and convincing council to hand over the power. Also there is really no need to talk much about 'coup' if you turned her down, she herself says that she probably will be dead and fail at the end of the road so...
Yeah she does, try choosing Conrad for the council and agreeing with the coup then you can see the exchange. If you antagonize her from the beginning, her plans won't rely on you at all, she won't even make you the offer so it probably involves something very different from the one she describes to the MC...