@lostagain,
What you're going through is to be expected, lostagain, all of it. The isolation, the anger, the disbelief... your whole world has been turned upside down.
No one can really advise you about what to do since every situation has its own uniqueness, but the right decision will come to you at the right time. It will just feel right.
Right now I wouldn't even worry about tomorrow - just live each day the best that you can. Just concentrate on you and your kids. Don't even think about the future at the moment - just focus on what you NEED to focus on.
This is a huge issue. It's a sort of death. The death of your trust, belief, faith, and surety in your relationship. So, treat it like that and grieve for it. Read about cheating, breakups, etc., when you feel inclined to, but not until then.
I had to deal with the death of a grandson and in the initial stages I couldn't stand the thought of reading about grief, etc., but one day I was ready to and I read some great stuff that helped enormously. It wouldn't have had the same impact if I'd read it the day after he died.
And time is a wondrous thing - eventually your mind will have absorbed and accepted all of this and then you'll be at the decision-making stage. Until then, just shove this mess in the back of your mind and delight in your children. Don't feel you have to sort it all out quickly. Take all the time you need. This has been a huge shock to you. All the future issues should be dealt with in the future (moving out, child support, etc)... right now, just process the information.
Keep talking and keep us posted, lost again.