First, we're not actually at war with Russia. Second, we're not even at figurative war over this. We have significant issues with Russia, like all large, powerful nations have issues with each other, but this isn't one of them. Russia allows the United States to adopt its citizens; that is a courtesy. It is also a courtesy that any number of Russians are sensitive about, the same as we would be sensitive if we were to find ourselves in the position of offering up our children for international adoption to any significant degree. So of course the Russian news media is going to make hay with this.
We simply need to be mature about the whole thing. Acknowledge the inappropriateness of one American citizen's actions, stress the gratitude many American parents have to the Russian government for allowing international adoptions, and move on.
May be you are right - growing in the USSR I am biased. The propaganda that Russians are running with stopping all US adoptions for investigation seems like insult to me, but I admit I am overly sensitive on the issue.