The kneejerk reaction of most newly betrayed spouses, particularly when there are children involved, is to try to save the marriage at all costs. There's a couple of problems with that though.
You have had NO TIME to process your emotions yet. You might get a couple of months down the road and decide this was a deal-breaker for you. It's a deal-breaker for quite a number of people actually.
There's been no time either to observe whether your WS is truly remorseful. Most of the time, what we see initially is regret. They're sorry they got caught. Usually, the affair is minimized and the truth "trickles" out bit by bit, often based only on what you can prove. There's typically a lot of blame-shifting going on in this stage as well as if it were your fault that she decided to cheat. Be prepared for copious amounts of crocodile tears.
The urge to do "the pick me dance" is so strong when you're in the Just Found Out stage. But if you do, she won't respect you and worse, you won't respect yourself after you've done it. This is the stage at which it's better to risk the end of the marriage and take your power back than to beggar yourself emotionally. There are worse things in life than getting a divorce. And should that happen, you can still be a great dad to your children and in time, find a more loyal mate.
First things first... self-care is critical. Eat right, hydrate, exercise, sleep when you can, and no alcohol. That's important, because alcohol is not only a depressant, but it has a nasty anxiety rebound the next day.
Second, see your doctor for STD testing and any medicinal relief you might need for sleeping and anxiety.
Third, see an attorney. Find out what your rights and obligations are in a divorce.
Fourth... inform the OM's wife. Like everyone else has told you, don't let your WW know you're doing this. If the OBS (other betrayed spouse) had told you back when she found out, you wouldn't be here right now. You'd either be divorced or reconciled. This is an understandable mistake, because sometime betrayed spouses worry that if the AP gets kicked out, they'll lose their WS, and they just want to hold on to the marriage so badly. Still, it's a mistake to cover their dirt for them because as you can see, they went right back to it.
I'll be honest with you, if it were me, I'd probably DNA test my kids and file on her. You wouldn't have to spend more than a couple hours reading in an OW forum to see how little regard a WW who has cheated for this long has for her betrayed husband. Filing will produce one of two results, either she'll pull her head out of her ass at lightning speed or you'll be free to move on to better things in life.
My fWH's last AP thought she was going to leave her BH and marry him. That would've been a financial step up for her, hence her interest. Turns out though, that when I immediately requested a divorce, my husband didn't want it AT ALL. He's moved heaven and earth since then to prove it. Meanwhile, the OW's husband gave her her walking papers, he's still a great dad, and he replaced her dumb ass inside of six months. She had actually told my fWH that if he didn't come through divorcing me that she'd have no choice but to work it out with her BH. I expect she was pretty surprised that he wasn't the patsy she thought him to be.
Take EXCELLENT care of yourself and your kids. Keep a cool head and an even temper. But don't commit yourself to taking her back until you've had time to process your feelings a little more.
ETA: If your WW is only doing volunteer work and doesn't have a paying job... get some day care lined up and send her to work. It will put you in a better financial situation in any potential divorce settlement and frankly... she's got too much time on her hands. Like my Grannie used to say, "Idle hands are the devil's workshop".
[This message edited by ChamomileTea at 12:00 PM, April 16th (Sunday)]