I think arsenaltilidie is more arse than anything else.
You do not say when you discovered this - just now; in the last twenty four hours; days ago.
If it is very recent, I suspect you will be panicking. What about the kids? If you've never divorced before - what is that about? What about the finances? How am I going to get a job after x amount of time out of work. What job can I do and and what about childcare? Will I lose the kids? How will I cope on my own?
It is a truly awful time for you, irrespective of whether or not you are the primary carer, or primary earner.
You will be in profound shock. In my own experience, the physical pain lasts much longer than the shock. Anger will emerge, and so will endless tears. For you, I have a lot of empathy.
What you need to do now is speak to a solicitor, if you can afford one (you being 'as a matrimonial unit' not as a SAHD'), or the CAB if you cannot as that will reassure you of what happens next, and what steps can be taken to ensure your immediate future is looked after from a pragmatic point of view.
It does not matter whether or not you file for divorce, or your wife does. I did not have to kick my husband out of my home, but hopefully others will be a long soon, who can explain more about this side of things.
Do not, under any circumstances, take revenge against your spouse. There is too much at stake for rash behaviour now.
Once you have spoken to a solicitor, it will help you see that whilst the emotional pain is still very raw, (I'm afraid only time heals), your life is a process of staged independence. In other words, your world becomes a matter of dealing with the pragmatics (calmly) and coping with the endless extreme emotions (which take time).
I hope this has been of some help to you. This is not about your decision to be a SAHD, it is not a gender issue. This is about being extremely hurt by the person you trusted the most. As I say, I do understand a little of what you are going through.