As a stepmother in a family that includes stepparents who married into the family when the children were grown, you (the general you) might be unpleasantly surprised by the amount of entitlement that comes out when a parent decides to remarry, especially
when a beloved parent has died and the surviving spouse has moved on. IMHE, it seems as though there is no agreement on what constitutes an amount of respectable time between the death and the remarriage. A year? 6 months? A decade? In my family, all have been fertile battlegrounds.
That being said, when I married my husband, who had teenaged children, we did talk to them privately before we announced our engagement to the whole family. However, no press releases were issued.
As others have posted, I think it's good manners and better for family relations if you announce to one's immediate family first, then "go public".