(1) It is better for you that you do not have any contact to your cousin rather develop friendly relation to her husband and ask the complete detail of their condition. And when it is clear that she is entitled to receive zakah then give him zakah money in privacy without telling that it is zakah and tell him that he may pay his debt from this money and may use it in his needs. If he takes the amount into his possession then your zakah shall be paid. It is not necessary to tell him that it is zakah amount.
(2) If they are poor then it shall be right to give this amount as well and you may adopt the same method which has been written above.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband