"Family day" is not an official WTS policy/doctrine and you will not find anything in the publications nor hear anything about it from the platform.
It is one of those secret, behind the scenes ways that individual JWs use to circumvent official doctrine.
True it is not policy or doctrine; however, it is also not wrong.
*** bh chap. 16 p. 161 par. 17 Take Your Stand for True Worship ***
Some parents set aside times to give presents to their children.
The picture on p. 163 shows a family with many wrapped gifts enjoying real happiness.
bczar