She told me today if I'd given her even a small fraction of the energy and love she needed this wouldn't have happened.
You're married 6 years, together 8, with four of her kids.
She cheated because you didn't give her enough attention (SHE RATIONALIZES) - this is the number one (I think) cheating wives claim they had an affair. It probably happens at least once a week here, maybe more. It also is very common for the betrayeds (maybe most people, in general) believe that their behavior can affect other people's behavior (if I do this, then they will do that). This is largely a falsehood with significant actions.
This is how it REALLY happens in a case like yours. The marriage reached a point where it became routine and boring. You still had regular sex, but you have day-to-day mundane interactions. Most of your interactions with your wife have become mundane interactions. Laundry, kid activities, work, extended family obligations, car repairs, finances, kids' grades, kids' sports events, etc. - this is most of the stuff you talk about.
When all the kids are in bed, you have a few minutes, maybe way less than an hour or less, to spend some time together. Maybe you have sex, then go to bed, and start it all up again the next day. AND YOU BOTH ARE HAPPY ENOUGH WITH THIS. NEITHER OF YOU DO ANYTHING ABOUT IT because you are happy enough about this. This is "NORMAL," this is the same stuff you saw in your own family growing up, this is the same stuff you saw your friends' family growing up, this is the same stuff you see with other parents in your kids' school, your siblings, your cousins, etc. I call this "LIVING THE DREAM." Kids are healthy and well adjusted, you and wife are healthy, no major continuing arguments, no drama.
Then, one day, your wife steps over the line with a co-worker or ex-boyfriend or acquaintance. Maybe your wife mentions something you didn't do ("how are you today?" "I'm tired, I had to discipline the kids, my husband let's them run rampant.") or maybe the other man makes an over-the-line comment (your wife is slow walking up the stairs and says "I'm sorry I'm slow" and co-worker says "I don't mind, I like the view" and your wife smiles and likes it.) This is how it starts. Then either or both of them escalate it. Within a few weeks or a few months it escalates to open ("you're so hot, if I could get you I'd do this, that, and the other thing," and "I love the way you do this or that").
Then the sex, then the I love you's between them, maybe to the betrayed spouse the "I love you but I'm not 'in love' with you." At some point, the cheater has rationalized "this other man desires me, loves me, and is all over me all the time about it, my husband only cares about paying the bills, if my husband showed me the proper attention then I wouldn't cheat, but I deserve this, my husband doesn't love me that way anyway, he won't even care, or any number of rationalizations. NOW the cheater is unhappy in the marriage only after the cheating had begun.
Then you find out. In this case, you found out ONLY because she had a Scarlet A in her uterus. She had a child with a different race, so this WAS going to come out sooner or later. She had decided to keep the baby, so you had to be told. If that had not happened, she may have continued the affair indefinitely until you caught her some other way. SHE DID NOT CONFESS. She had no other choice.
So you find out, she blames you for lack of attention, and you believe it, and you know where you are now and how that all played out. The truth of the matter is that the affair is an escape from reality, and there is no way a real marriage can compare with a fantasy affair. The real marriage has chores and kids and finances and problems, while the fantasy affair has only I love you's and you're so hot and sex. If the fantasy affair became a real relationship, it eventually would turn into another long-term boring marriage.
Cheating is a human behavior, and as such, it is very predictable. The behaviors are within very limited ranges, and your wife is a cliche. The only somewhat unusual twist is the pregnancy with a race from a different affair partner (consider that if the affair partner was the same race as you, you would never know; the only reason you know is because your wife could not lie).
She told me today if I'd given her even a small fraction of the energy and love she needed this wouldn't have happened.
So this quote, what she told you - this is the mindset of someone who will cheat again. You must give proper attention, or she will cheat - that is her assertion. Also, the next other man, like the last one, will give full nearly 24/7 texting/sexting focus on ONLY romantic/sexual attention and you still will be needing to, as you say, "LIFE MUST GO ON" - work, chores, finances, kids' activities - so you cannot compare against the future other men who will inevitably blow some smoke up your wife's ass.
My only advice to you is to understand what is going on, what has happened with others in the past in your situation, and that you and your wife are not different in that respect.
Your wife is not a safe partner to remain monogamous in the future. Not at this time.
You have left out much details, but I would be curious what happened with the biological father(s)(?) of your kids. What happened with your wife's past romantic relationships? And yours? I believe if we do not focus on change, we tend to continue the same behaviors, the same patterns.
The main signs you would have noticed during her affair would be secrecy with her phone, and cold and distant toward you, and everything you do or say she is annoyed. She maybe had special lingerie, different grooming, dressed sexier, exercised more, lost weight, less interest in sex with you, or more interest in sex with you.
Who is the other man and why do you think the affair has ended? Why do you think it will not start back up again? Will the biological father support the child financially? Will he be involved in parenting the child?
One of the main things said here of how to reconcile a marriage after an affair, is that the cheater goes "no contact" with the affair partner. Just a coincidence, the pregnancy, this makes the "no contact" impossible. Legally impossible, unless the other man voluntarily never wants to meet his child.
Have you come up with a plan? Any number of factors that could let you decide one way or the other?