If you’re going to make shopping while people are being slaughtered a war crime then half of Syria will be in the dock. Not mentioning in emails that you are opposed to the slaughters may be bad form but again, it’s no war crime. Being married to a war criminal isn’t a war crime either.
It’s pointless bringing up Mussolini’s mistress. She wasn’t convicted of war crimes, she was hanged by the partisans, who themselves could have been charged with a war crime for so doing.
War crimes, as defined by international law, are very specific. It isn’t just a case of convicting someone of not being a nice person. I think it most unlikely that the Syrian dictator’s wife will be charged with war crimes.
BTW I’m talking of international tribunals here. If she’s captured by Syrian rebels then they may well execute her simply for being married to Assad. But that has nothing to do with war crimes as defined by international law. (And again they should be very careful of international law themselves in their treatment of her.)