Your wife has done what I call "hitting the wall." It happens to people who have stuffed issues rather than deal with them. Odds are the original issues are not with you. However, when things are stuffed, anyone can become the personification of those issues--and at time it does feel like someone else (you or the kids or the boss at work) is responsible for her being sad. Then there are more lucid times, when she realizes the feelings come from within.
Since she's not yet ready to face what is going on inside her (a civil war), you won't be able to figure it out either. And even more importantly, you can't put any weight on anything she says about it--except that she may leave. She is running on the inside and the outside may follow. It doesn't even matter if it the right thing for her to do or not. People who hit the wall are liable to do almost anything--and by the time they admit--they are pretty well out of control of their mind. It's not crazy--it's fear, emptiness, and often self loathing.
What you can do is listen when she wants to talk--and NEVER take issue, NEVER try to explain, NEVER question, or react in anyway other than INTERESTED. Learn to say, "oh" a lot and in a lot of different voices. Say that's interesting, I never thought about that, I think I see what you are saying, (not just, I see ...). If she mildly complains about someone or something don't ask questions or try to solve it. Say things like, I didn't know she was like that or it sounds unfair to me.
Think of her like a baby without a vocabulary. If a baby is crying you don't ask questions, you don't give advice. You pick it up and rock it. You pat it's back and hold the baby til it finds peace.
Obviously from your post you would be happy to hold your wife and make her feel better, but she is rejecting. However, there is a way. When your wife is calm, touch her on the right shoulder. Make it a firm enough for her to feel--almost a squeeze--and then let go and greet her with simple words or a smile. After a few times, if she accepts it, start doing it everytime you see her--in the morning when you wake, after work, after dishes are done. What it does is say I'm here and I'm the same as always. It gives both of you what becomes a common, non-threatening moment. She will probably ask why you are doing that--tell her I would love to just hold you and make you feel better, but I don't want you to think I expect anything from you, so I touch your arm. I guess I'm trying to show you. (Or something like that.)
She will fall behind on things that are important to her. If she is a clean bathroom freak--make sure you leave it clean. If she couldn't care less if the windows are washed, but you do--don't wash the windows. Tell her you realize that she's down, and you want to help with the house and kids, so could she please make a little list for you of what she would like done. Then tell her when you will start and finish the list. You don't want her seeing you do the work--that's depressing--and in the state she's in, she will balk. But if it's magical, she may accept it.
You may or may not try this--use judgement. Have her take the kids (or one of the kids) some place. Start with a place that she used to go often or which is only for a few minutes--and build it up from there. While she is gone, do something from the list.
Odds are that you got taken by surprise, because she is complaining to someone. You need to bust into that--alittle. If you make the separation too great, that's all that will be on her mind--so that does you no good. But keep things stirred up with as many good, happy things as you can. Talk about pet things from the past, remind her of things she liked. (Look at photo albums for ideas.) And don't be surprised if she says she hated something you think she liked. Right now it needs to be all about her--and if the past memory is about going to your car races or the kid's t-ball game--it's not about her--and right now she will hate it.
I've seen this sort of battle before and most of the time, hitting the wall in the way your wife did is a bad sign. Too many of those women walk away from really great guys and lives. I'm hoping that the meds and counseling will prevent it this time.