Whitetail deer gestation is aproximately 200 days or 6 1/2 months.
Lets say they were about3 months old. This would put conception
around March. This is unussual but not impossible. A deer comes into heat
in late Nov-Dec. If she is not breed, she will come into heat every 28 days until she is breed. So in answer to the "second" birth, she may have a birth any time of the year. Just depends on when she gave it up.
By the way, no I would not shoot because if they are still in spots then they are most likely nursing too.