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, if by your statement “I am paying Zakah” you mean that you pay it from your own money, then you should know that you are not obligated to do that. Also, this is not sufficient on behalf of those on whom the Zakah is due unless they authorize you to pay Zakah on their behalf, because it is a condition (for Zakah to be valid) that the owner of the money has the intention to pay Zakah. Therefore, if you had paid the Zakah on their behalf with their permission, then it is permissible and it is sufficient.
Also, the method which you follow in paying Zakah is not correct. What is obligatory is to deal with the gold of each one of them (your mother, wife and daughter) separately and then pay from it 2.5 % or you may pay its value from her other money if the gold reaches the Nisaab (the minimum amount liable for Zakah) by itself or by other money or tradable items and the like which she owns.
Therefore, you should pay from the gold of your mother 2.5 % which is 4 grams or the value of these 4 grams. As regards the gold of your wife, you should pay 2.5 % which is 12.5 grams or you pay its value.
However, there is no Zakah on the gold of your daughter because it is less than the Nisaab, as the Nisaab is 85 grams of gold, unless she has other money or tradable items to complete the Nisaab.
For more benefit, please refer to Fataawa 154387, 88256 and 102345.
Allaah Knows best.