Regardless of whether a threat to self harm is genuine or not...In my view it is a kind of wish, and most definitely a cry for help, which should always be taken very seriously. I would encourage her to get some counselling, and maybe inform one of her friends or family members that she has been making threats to self harm. Coming clean about the whole situation with everyone involved (including your wife) I believe will go a long way toward starting the 'damage control' process.

Good Luck to you moving forward Otherworlder92, and welcome to P.C