The blue star in WWII in the window of a home indicated a family member killed in action.
No, the blue star indicated a family member in service. In the case of death of said service member, the star color was changed to "gold". Most of the stars were sewn on, so one would have to sew a gold star over the blue star. I have one banner, however, in which the stars were "cut-outs"...it came with both a blue and a gold card to tape behind the cutouts to indicate the status of the "son-in-service".
The "Gold Star Mothers" group in WWII was comprised of women who had lost a family member in action.