I believe you do not need re-stamping as you will be working for same employer, same role and same location. As there is no change in working conditions, no need to get it re-stamped.
There is no problem if you delay your departure after visa stamping. Some of my friends have gone after 3-4 months too.
Why don’t you get H4 stamped for your wife and kid along with your stamping? It is easier that way.
For some personal reasons I wasn’t able to initiate my wife and kid’s H4.
Is it possible for a group interview(if mine is already stamped), or they have to go on their own?
Once the visa has been stamped in the passport, no further stamping is required until its expiration date.
Your family can attend the interview with you (you cannot add them to your current booked slot unless you schedule another interview date), or they can go separately later.
It is ok to travel to US few months after getting the visa stamped. However, you should always carry recent documents when traveling to US.