I am so sorry to read about your situation and all that you're going through. Not only are you grieving through this separation from your wife, but you are (understandably) worried about your children....and....you have to work with your wife and this other man. I can only imagine how devastating this is for you, and my heart really goes out to you.
I would encourage you to talk to your doctor about the possibility of medication, and whether or not he/she thinks it would be warranted. Perhaps you should also ask about some counseling for yourself, to help you to deal with this very stressful situation. The idea of divorce, whether it happens or not, is incredibly difficult to handle, and having children in the mix brings an even greater emotional impact. It is also important that you are able to continue to work, and you may need some support in dealing with that, as well.
Whatever your wife decides to do, it is in her hands at the moment. You may not be able to control what she does, but you CAN control what you do for yourself, to help yourself and your children to cope. I hope you will consider talking to someone about this....your doctor or a therapist, perhaps..... because you deserve all the support you can get, and you need to take good care of yourself to stay strong and well.
Please know that we're here for you, and will do whatever we can to support you.