At first when I read your question I was thinking oh no here we go with some kissing story but let me help my readers, this is her cousin from her husband’s family.
In the letter she states that her husband had invited him over and they had way too much to drink meaning her husband and the cousin not her. So when she was getting him some sheets as he was too drunk to drive he began hitting on her. She didn’t say anything but the cousin mentioned what happened to her husband and now the husband thinks she wanted his advances.
My advice is your husband is over reacting. If it was me I would have spoken up right away regardless if the cousin was drunk or not. However since she hasn’t I would have reminded her husband that her cousin was drunk she didn’t flirt back and dismissed his drunk behavior.
I would tell my husband that he either has to believe it or not. You were upstairs with him the entire time and nothing happened so his ego is bruised because he wants to side with his cousin who obviously is messy. I definitely would tell your husband that you don’t feel comfortable with the cousin staying over anymore.
If after you have explained that happened know in the back of your mind not only what type of man your husband’s cousin is but never allow yourself in a room with him again because he will lie when it’s convenient. Also makes me think your husband has had conversations with him about your marriage which made it easy for him to lie and get in your husband’s ear. Hopefully after your husband has had a sobering moment beyond the alcohol he will come to his senses and believe you. Although there will have to be a lot on his part to repair the non trust he showed towards you. If he really felt you would have kicked it with his cousin but he still married you he has issues and I doubt that’s the case.
Lastly the cousin told him he hit on you and your husband didn’t say anything to how wrong he was. Let’s say you did take his advances wouldn’t his cousin be just as wrong if not more?
Again your husband wants an excuse. Don’t let him. If he wants out let him go but it sounds as if he allowed his cousin to hype him and have you take the blame. You did as a wife was supposed to do with any man which was ignore and dismiss his advance. The only issue I could see was you not saying something when it happened. You have to be the first to speak especially when the perpetrator is in your own home no matter how innocent it may be to protect yourself.
Good luck to you