Do NOT do this ^^, very bad idea.So there are two ways to approach this.
The first way is to complain, which you are doing. Endlessly analyze the situation, look for clues, blame yourself, etc. Try to fix it through "acts of service", placating the wife, talking with her, etc.
None of that is going to work, and will only make matters much worse. That is the weak man's approach.
The second way is to take charge of your life and improve your situation. It starts with recognizing your value as a man. And it involves actively embarking on a strategy to fix the situation one way or another. Immediately begin to do the following:
1. Get in the best shape of your life. If you are already thin and athletic, great, now start hitting the gym 5 times a week. Take supplements, run, pump iron.
2. Set aside some money to get yourself an excellent wardrobe of clothes. Go to a designer store and ask one of the guys working there for help. No more wearing backwards baseball caps and old t-shirts: dress like you are actively looking for female companionship and you want to impress.
3. Go to the best hair salon in town.
4. STOP doing things around the house: no more "acts of service", cleaning up her shi*, catering to the kids.
5. Lock your phone and your social media--no wife snooping
6. Start going out at night with friends to events, clubs, bars, games, whatever. No "checking in" with wife, and stay out all night if you want.
7.No sex or affection with the wife--she is a roommate going forward. If she initiates (which she will do after a few weeks) shut her down without explanation.
Now a few things will happen after a few months of this:
a) she is going to complain about you not doing enough around the house. You respond with "I make enough money to support us both: why don't you quit your job and stay home"?
b) she will start initiating sex and affection when she sees you slipping away. This isn't real: she is trying to rope you back in, and if you fall for it, it will be right back to dead bedroom.
c) she will want to talk about it. You refuse until about 6 months in. THEN you sit down for the hardcore discussion.
and that will either lead to divorce or some kind of reconciliation.
Your wife feels she "missed out" by stating with you in her 20s and ultimately marrying. She resents her loss of freedom, and wished she could have slept around with bad boys when she was younger like many of her friends did. She's bored and restless.
so she will either realize what she is going to lose, or keep on with this game. You need to stop being afraid of the consequences and get in front of this
The reason that nicing your way to sex won't work, is because she knows you're not doing those extra things out of love for her, but to get something in return. It takes away any feeling of being grateful.
What you need to do, is organise someone to care for the kids ideally overnight, but if you can't swing that then a few hours. You need to lay it all out on the table for her, how you're feeling, why you're feeling that way and what you need from her. Then, you ask her how she's feeling, why she's feeling that way and what she needs from you. Get it all out there from both sides, the good, the bad and the ugly. Then work together move forward.
I find it strange that you didn't have sex while she was pregnant. Unless it was a very high risk pregnancy, there's no reason for that - I wonder if your wife has some anxiety, and it's now coupled with PPD. That would explain a lot.