This is SO easy to solve without any of this "for plot" bull x.x
The Mileton Household is making this offer because it's financially beneficial for their practically broke ass since they no longer have Agatha to look over their finances. Thus they claimed that they would "offer" her to him as a concubine if given a proper "donation." Since she's already an integral part of his diplomatic efforts, getting up in years, and has great qualifications nobility would see it as an insult for Balud to NOT make some sort of offering if he plans on hording her abilities when she's already at that age. With the backing of two major noble families, Orkney and Hastings, it also emphasizes this point. Solution? flattery ^-^
"As part of the esteemed Mileton house and with her immeasurable capabilities, I'm afraid that making Agatha Mileton as a mere concubine to the Visconti of Antrim would be unacceptable. Indeed, for one such as I, marriage would be the only way I could possibly bring my worth to equal hers. Unfortunately, I regret to inform you that the Antrim Viscounti is currently 100 thousand gold in debt to the dowding company and, thus, not in a financial state that could bring a madame as great as Agatha Mileton, the elder sister to the house of Mileton, the life that she would deserve. Once this debt is settled it shall be I who will take the opportunity to pursue this matter further, as is what is best for the Mileton Baronet, the Antrim Viscounti, and most important of all, your elder sister Agatha. As a potential brother-in-law it would be most appreciated to receive any aid, financially, military, or diplomacy from the magnanimous Mileton house as Antrim prepares for it's inevitable confrontation with our neighboring, hostile, nation that has been showing signs of imminent invasion. As a close ally to the great and powerful Orkney and Hastings families, it would do good in protecting not only our country but also your magnificent sister, Agatha Mileton, talking to them of such aid would also be greatly beneficial to her and the Mileton's future."
Yeah, turn Orkney's letter against them as well... since they promoted the union now they are in a position where if Mileton revokes their absolutely horrible deal, they lose face as well and you get off scot free. The Mileton probably won't last until you pay off the 100k with him as the head and even so you never guaranteed you were going to marry Agatha, just that you would be the one to pursue the matter. To other nobles that are unaware of the situation it looks like you are evaluating Agatha even HIGHER than her brother and are even holding her household on a pedestal. You then recognize the individuals who promoted the union as people of much higher position than yourself. You could say that part of the reason he couldn't accept her as a mere concubine was BECAUSE Orkney and Hastings were backing the idea. Not only does that letter fuck over everything, it pulls a complete reversal on the situation, not providing aid is the same as saying you don't actually believe she's worth anything, canceling out any need for a bride price if he doesn't provide anything ^-^