All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, you should know that it is not an obligation to pay Zakah on money unless it reaches the Nisaab (the minimum amount liable for Zakah) and a whole lunar year elapses over it. The Nisaab in money is what equals 85 grams of pure gold, or 595 grams of pure silver or what reaches the value of the Nisaab of either.
Therefore, if you had spent this money on the construction of the house before a whole lunar year elapses while it is in your possession, then you do not have to pay Zakah on it. However, if the money stayed in your possession and you did not spend it until a whole lunar year elapsed over it, and it reached the Nisaab, then you are obligated to pay Zakah on it. This is whether the money is in your hand or given to your brother-in-law, as it is an obligation to pay Zakah on it if a whole lunar year elapses before spending it.
As regards the rent you will get from this house, then you are not obligated to pay Zakah on it unless a whole lunar year elapses over it (i.e. over what remains in your hands from it) as we have mentioned. So, if a whole lunar year elapses on it and it reached the Nisaab even by adding it to other money that you possess, then you should pay Zakah on it without deducting the debts that you have to pay according to some scholars and this is the best option in order to be on the safe side and be acquitted from sin. However, the majority of the scholars are of the view that you should deduct the debts that you owe and then pay the Zakah on the remainder if it reached the Nisaab. This is whether these deducted debts are from the money that you owe/pay for rent or else.
Allaah Knows best.