Beagle... you're at the start of a long row to hoe. It's going to be rough.
Right now you're still in the numb and disbelief phase. It's hard to believe how so much can happen so fast that affects our lives in such big ways.
You're at the start of the "emotional rollercoaster". Moods can shift (and usually do) from disbelief to anger to depression to anxiety to a feeling of worthlessness, jealousy, hate, grief, uncontrollable crying and gushes of love, sometimes these come in rapid succession. It's one hell of a ride.
You have gotten amazing advice on this thread from some very seasoned individuals who know so much about cheater behavior that you wouldn't believe it. All cheaters have what seems like a common play book. They become almost predictable. BS response has a playbook as well. Left to our own devices our immediate response (due to the immense disadvantage of weakness, numbness, pain and hope) we can make some VERY bad early decisions. The worst: jumping right in and starting with excuses or seeking reasons of why it happened that involves other than the cheater and then thinking oh well it's over, lets rugsweep.
Some of the advice is geared toward end game. You're not ready for that kind of decision yet. Some go D, they know, over, done, move on.
Others aren't inclined to end things on the spot. They have conflicting reasons. It takes them a while to decide.
When an R situation is on the table it's generally advised to be non committal for at least months. Six months is soon enough to decide what this M is going to be from here on, if there is going to be one. It allows the worst of the first waves of emotions and pain to subside and it's easier to see the real landscape, the spousal response and their attempts at fixing themselves. Be careful: she's pushing this stuff where you have to change. Hey, you're not perfect. The changes you have to make are tiny if not zero, the changes she has to make are gargantuan. She was out there risking insemination by another man with a one year old. That's really down the trail.
Take your time, take care of yourself and protect yourself (accounts, etc) in the event it goes D. You first, then your kids, and her in the far far distance back there somewhere.
This is up to you, no one else. Believe this: you are not in the life you used to be and won't be in that life the way you were, ever.
Expect her to be lying, minimizing and blame shifting. The more defensive they are, the more there is to hide. Expect it.
Please don't rush, you don't have to. Please take care of you. Please read about the 180. Understand it. On this site there's plenty on the 180. A search for 180 infidelity on the internet will get you plenty more from all over. It's the best treatment for these cheaters. They either are pushed back into reality or they leave the marriage. When they leave, they should, for they're no longer in it enough to care about it.
Good Luck. We're with you. We have ALL lived some version of the hell you are now going through. So many of us wish we had started here.