I think LadyC is correct, although she and I both know that sometimes marriages come to an end. If that is the case, now is a very good time to break the news to your husband. You should do this before you are any more wrapped up in your cousin. You really put us in a bad spot when asking "should I leave my husband for my cousin." The short answer is no, of course.
My wife and I have been on and off for years. Two years ago, I decided to try again with her -- not because it was easy but because it was hard. There was a whole lot of crap to get past and to process. The experiment didn't work out but I am glad that I gave it one last shot. Is that an option for you? I suggest that you give it another try with your husband, maybe go on a cruise. In my opinion, you should keep the affair to yourself and take it to your grave. Look, if it doesn't work out, then do it right. Leave your husband before you start back with your cousin.
Second marriages statistically are more likely to fail than first marriages. If you keep carrying on with your cousin, you may very well end up with nothing but a lot of heartbreak. I would hate to see that.
Affairs are a great way to burn bridges. You are sabotaging your marriage. Are you sure you want to go down this road?