If your sasur (father-in-law) is eligible to receive zakah, you may give him zakah money. You should give the zakah amount in the complete possession of your sasur in case he is eligible for zakah since tamlik (giving in possession) is a condition for the payment of zakah. Then if he gives you the amount for his treatment you may spend it for his treatment. You should not use it in his treatment on your own. Yes, you may give him medicine purchased with zakah money.
Allah knows Best!
Darul Uloom Deoband