I have read through this whole thing this morning, and I have a few thoughts. I may come off as crass or abrasive, but I am trying to take the emotion out of it, so you can step back and look at it like an outsider.
Your wife, had an A, she chose, yes she CHOSE to have an A, she didn't just fall on some guys junk and say woops. Then she recklessly didn't use protection and is NOW pregnant.
Things we don't know for sure.
1. When she became pregnant. (I say this because you mentioned she hasn't been to the Dr yet, and really until they check levels, and do a measurement by ultrasound you are NOT going to know for sure. You CANNOT, trust her dates bullshit because she has proven one thing. She lies.
2. She is claiming it's his, but had sexual relations with both of you prior to announcing her pregnancy. You have approximately 2 weeks from the time you conceive until you get a positive pregnancy test. I suspect she knew or guessed she was preggers a while before showing you the positive test.
3. What does she gain from acting like it's his baby? Well lets see. She gets to continue to interact with him and keep her relationship alive with him, because right now she is getting to play aren't we a happy couple we are having a baby with him. She also gets to blame you and "working a lot" for her actions, and hasn't committed to R'ing because she hasn't had to. She has the best of both worlds at the moment.
In most situations I encourage the BS to stay away from their spouses AP because they usually try to say thing that will hurt you. HOWEVER....In this situation, I think if you picked up the phone, and said I want you to back the hell off, and have no further contact with my wife, the baby isn't yours, she is just trying to string you along, the sigh of relief that he would have would be heard around the world.
Your wife, doesn't get it yet, and may not, but I think it is time you went and saw an attorney, to find out your rights and obligations, and file whatever paperwork you need to to make sure that your kids come first in all you do. The only thing she is sorry about, is getting caught, the only she is sad about is having to give up either her boyfriend, or her spouse.
You need to take a step back from this and think about what you really want, and why, and "Staying together for the kids" isn't an option. All that does is teach them dysfunction, and gives them a false sense of what a normal happy relationship really is, which in turn messes them up and creates generations of this fucked up sense of what marriage, commitment, and loving someone is all about.
Your wife, is NOT putting her kids first, and it's your job to call her out on it.
The R car should be driven by the BS, and if it's not that long curvy journey ends up in a ditch 9 of 10 times. The WS, yours, mine, and everyone elses here all have one thing in common, they are broken people who have a lot of work to do to heal themselves, and until they start that you are setting yourself up for failure.
(((and strength)))