Often times we get stuck in the what-if and it comes with a lot of anxiety and worry about trying to find the "right" thing to do or say. But what helps me is asking myself the question, "wouldn't you rather know?"
I've been denied by many beautiful women and I've been accepted by others I never thought I'd have a chance with. The only ones that I regret are the ones I never had the courage to ask. Life's short my friend, don't burden yourself with worry and wonder. Give it a try, just ask her honestly and be ok with whatever the answer is.
If she just wants to help with the house? Great, you have a better chance of becoming friends now that you're not worried about what she thinks of you. If she's unsure or says yes, then just let things develop as they will. Worst case scenario, she doesn't talk to you anymore...sad yes, but at least you can look for someone who wants you back!
How old is this cousin? Maybe they don't know how to deal with difficult information yet