Well you explained yourself perfectly well here, i think if you tell them exactly as you have here you will be fine, your cousin sounds like a sicko, and her word against yours is conflicting statements, in court the judge would throw this case out, i wouldn't worry too much, if your parents dont believe you, i would tell them what she was trying to get you to do or let you do, she sounds like a bit of a drama queen and a *****, stay away from her.
By the way i disagree with your parents, there is absolutely nothing wrong with masterbating, and that is disterbing how ur mum went off at you for masterbating, dude materbate all you want, your not hurting anyone and its a good way to stop sexual frustration. Just dont let ur mum catch you ;)
I don't understand what advice your trying to give her daisy. I think you should refrain from giving advice. to anyone. "and if nothing works,undress her & try weird stuff." Your sick.
Anyways. Try to convince your mother, avoid your cousin and do not have anything to do sexually with her. She can lie all she wants but there really isn't any proof of anything. Make it clear to your family that she's tarnishing your reputation, nothing happened and you will be avoiding her because she's a liar. Even if they don't believe you, the evil she does will come back to her.
Soon enough they'll begin to see the type of girl she is and her true colours will show. I'm sorry that you've gotten into this kind of trouble but you know what happened, so don't worry about it too much. You don't need to feel guilty for something you didn't do.
Take care and I hope that this helped, unlike other peoples rubbish advice. :S