I now feel like I fully understand where our main character is coming from, first off we have her upbringing, it's clear she's grown up with the idea that nobody could ever love her, and that any affection towards her is to keep up appearances or out of convenience (and in the case of the marriage, that sounded like he only married her because of a promise to his father)
Then there's the male lead, who has done an absolutely piss poor job at clearing the misunderstanding, it's not just his new wife who thinks his cousin is a lover, literally all of HIS servants also believe it, emphasis on these being his servants, they're not outsiders who just met him, this has apparently been an unspoken understanding in his mansion for years
Also, notice the parallels for their reason to marry: she was told by her father to secure the marriage for political gain, what she got out of that conversation with her husband is that this was also forced on him by his own father