Carlota spends more time strategizing to meet the paladin Alexaera Cansellarion than almost anyone else. The Archdukes you can just invite to parties; she's worried that inviting a paladin to a party in her Magnificent Mansion sends entirely the wrong message, even though she's donating the excess food to the poor and it was actually not more expensive than a city home and adequate security for it. And the Archdukes are mostly natural allies in politics, sharing her interests in peace, stability, prosperity, alliances among each other, and digging their country out of its hole. A paladin of Iomedae...probably has many interests in common with them but belongs to Church more than country, everyone knows that.
Carlota would rather like to be a paladin of Iomedae. It runs in the family, and she has the charm for it, and there is no stronger form of moral authority in Cheliax than Iomedae's blessing. Unfortunately Iomedae seems to have all but stopped selecting paladins. Perhaps Cansellarion knows why. And perhaps he can give her a hint as to where the Church means to stand on the major controversies of the convention.
She has a spectacularly good diplomatic gift for him, but still needs to arrange actually meeting to give it to him. Eventually it is the Archduke Narikopolis who gives her an opening for it, by having her to a dinner she boldly arrives at an hour early to have the chance to speak privately with Cansellarion. (Yes, he's in; she may have had a servant follow him through the streets to confirm it.)