There is a forum for 'sex, love and relationships' here so just a heads up your post might be moved.
Now onto the issue at hand,
I cannot tell you to break it off, or work at it and stay together, it is not my place. It might sound old fashioned or even cliche but one of the biggest problems in relationships is communication. You need to make sure she clearly understands and can meet your needs (and wants) and vice-versa. The best thing I can suggest you do is sit down and talk it over,
openly and honestly, but before starting this be prepared for either outcome. Try to keep as calm as possible during the talk (easier said than done), but if you are just yelling at each other neither of you will listen.
I will say this though, the part with the cousin she may not have intended to mean it that way, but yes, a lot of guys would think like that, you need to talk to her about it and make sure she understands that it hurt you, and next time something like that happens you want recognition. You can be somewhat demanding but be open to a little give and take along the way.
I'm sorry you are in this situation, especially if you love the girl. But in the long run if you are left constantly feeling broken down, bruised, betrayed and/or sad then honestly it isn't worth it. Relationships are one of the hardest parts of life but can also be the one of the best parts, of course they can also be one of the worst parts too. So hang in there and make it clear she knows how you feel about this and what you want her to do about it. At the same time listen to her side of story and see if you can compromise.
Start thinking about and visualizing in your mind how the talk will go, think about the answers she might give, in either direction, and how you will react, and what it will mean to you. Don't be ashamed to put pen to paper and dot down key points if you need to - but don't use it to quote arguments from the past etc like "dec 21 2012 you said "I don't like fish" - haha, doing something like that will most likely seem like a planned attack and whilst planned this is more of a negotiation.
Lastly, you mention you've been wanting to break it off. I want you to stop for a moment and think, at the end of the day, when all is said and done, what do YOU want? Run through a few scenarios in your head...where do you want to be in 3 months time? 6 months? 1 year? 5 years? and who do you want to be with. Her? Someone you else you know? Anyone else? or even by yourself? Whilst it's completely true relationships are about sharing and fairness for both people in the long run each person has to do their best to put themselves first. Also, during these visualizations/thoughts etc think about how marriage fits in to YOUR life, is it something you want? With Her eventually? With anyone?? What about kids etc. If you find it helpful you can write some of this down as well. It's then up to you if you let her read any of it, or if you keep it to yourself. Both are completely valid and understandable options.
Next think about spending your life with her and think about what the best and worst parts of this would be. Has this issue been coming up since the start of your relationship? Is it more of a recent thing? What happens if it gets worse? What happens if it never happens again? etc... again, think and optionally write down your thoughts.
I know it might seem like a lot of work but it's really the only way you are going to know the answer. Yes, it can come down to cognitive dissonance or even head vs heart, but doing practical activities like I suggested above can provide you with a much clearer framework of what to do, and how to do it.
Of course you don't HAVE to do any of this, I'm just suggesting it as a possible strategy to help you and her work out what is wrong, and how to fix it, or at worst, decide it is not fixable, or not worth fixing and that way you have a rational, logical reason to continue the relationship, or bring it to its conclusion.
TL:DR:
Think --> Talk --> Try -->
If(Success) then
Win
else
Quit
Best wishes and good luck, now and in the future.
Namaste,
mysticbeef
P.S Just wanted to add - be careful when organizing this talk - make it a neutral location for both of you and a time when neither of you are particularly stressed out over external events. Eg: Not at your mothers house christmas day, she'd probably see that as unfair (based on location) and it's more stress on the both of you.