It sounds like she is happy to move in with you, and while she may be skeptical of such a big move, she did say she didn't care where you live as long as you live together. But suddenly you tell her that your cousin is moving in with both of you and you expect her to think that's awesome? You completely made that decision without her. You didn't even ask her if she was cool with the idea, you blatantly told her that was the new game plan. You said he would be the third wheel, but it honestly sounds more like your girlfriend would take on the third wheel role, and it sounds like she senses that as well. Anyone in their right mind would be annoyed by that. I can see where you're coming from in the reason why you want him to join you. Having a support system in new environment can make the transition a lot easier; however, your big mistake was that you decided this without talking to your girlfriend first. A big lesson to learn when you want to take the next step in your relationship and live together, means you need to talk about everything and make decisions together, especially if they are going to affect the other person.
"Caring is not an advantage."