Your right.
First, the loan is between your cousin and another person. At this moment, you are not a party to their contract of loan, so you are not obliged to take your money out to pay the loan.
Secondly, the agreement that you will help your cousin to pay her loan, provided, your cousin will pay you first is a valid and binding contract even it is done
orally.
Third, your cousin's complaint that you did not pay your part of the loan is ridiculous. Dont be threatened, just leave it alone, it doesnt matter whether your cousin have a hundred of witnesses, still you cannot be obliged to pay her loan, because of the above mentioned reason. yung first.
Fourth, you cannot consider your verbal agreement with your cousin be null and void, it is a valid contract, however, your cousin cannot enforce that contract unless and until, she pay you first, that is a suspensive condition (the happening of the event, give rise to an obligation), so, as long as she did not pay you first, then you are in no obligation to pay the loan jointly.