Part of me wants to say "Turnabout is fair play" and to go for it. However, doing so will only deepen the rift between you and your cousin. I wouldn't want you to do something that will end any chance of reconciliation between you two.

Then again, the two aren't dating anymore and she is available, so yeah. Also, don't just date her to get back at your cousin, it's not fair to her to be the revenge girl. She's already been treated poorly by him, if your post is anything to go by. Only date her if you truly are interested.