1. Get legal advice, fast. 2. Do not pursue your wife. 3. Show back-bone and resolve. 4. Believe that she wants a divorce.
If she sees you are preparing yourself, emotionally and practically, for a divorce, she will realize she's playing for keeps. You won't come back crawling to her. Her actions have consequences. This will show strength. Don't be an a**hole, but, remember, you are not her best friend or husband anymore, not UNTIL she says she wants back in to the marriage. She just came off an emotional affair(probably a physical affair).
Start using the Last Resort Technique.
Decide you can "wait" in terms of divorce action for a limited amount of time. If she's pressing for a divorce and you are dragging your feet, (either trying to save the marriage OR not sure what you want) it will get ugly.
Most importantly, under the assumption that you are getting a divorce, be clear and know WHAT YOU WANT. I kid you not. Don't be ambiguous.
If you are not rich, you can't afford a knock-down contested divorce in court. So...once you know what you want, make your wife an offer and stick to it. If she doesn't accept your proposal then get yourself 2 Lawyers to agree to practice collaborative law (who refuse to go to court and fight. It's a form of divorce law.) If they do that, find a good mediator, come up to a fair agreement, and then have a lawyer look over the agreement and sign.
Your wife's good will now (pretending not to want anything3) will erode once she's talked to a lawyer.
Now here's my personal observation. I've been on the DB boards a lot in the old days. You've had the Divorce Remedy in hand the first time around, you went to Retrouvaille and did some triage in the marriage after the first affair. The marriage deteriorated again and she's in a second affair and wants out AGAIN.
I've seen this scenario several times. Even Divorce Busting superstars (who used to coach us with their success stories) who saved their marriage the first time COULD NOT do it a second time. Their wives wanted out, and cheated, AGAIN. It plays out one of two ways: you either hold on to a spouse who wants out and end up losing everything (including your house) OR you accept that this person doesn't want to be married to you and isn't faithful, and you move on successfully through a fair settlement and divorce. I know two superstar divorce busters who ended up in divorces the SECOND time their spouses chose to cheat. One ended up frozen like a deer in the headlights and lost his house, the other actually "led" his wife through the divorce and came out a champ.
Sorry to say this, but a repeat cheater is not likely to be a good long-term spouse. It's not about you, dude, it's about her.
On a more personal note, I was lucky. I came out with a good settlement. Shared child custody, paying minimal child-support and no alimony. I thought I busted my divorce. Then a couple of years later she wanted out again and started cheating. My only regret: not having divorced her the FIRST time around. I wasted years of my life.