First off, I am frustrated just reading about your journey. Now is the time to act "as if." Time to act as if you are moving on so it becomes a truth. Your wife has zero respect for you and is basically keeping your testicles in her purse. You need to show your children that a father and husband is supposed to be strong and dependable.
If your wife wants to go to grad school and check out of her kid's lives then by all means, step aside. Start setting up childcare when you have things to do and she refuses to parent. She wants a divorce? Fine, act as if it's in process. This means setting up child custody exchanges (I've recently made it clear to STBXWH that he will be responsible for arranging child care on his weeks) this had the result of shocking WH. He backpedaled and tried to assume I would take them if he had to work late and I clarified that it would not always be possible. I also sat down and had a talk about the splitting of assets, I am being fair and not spiteful but I get the house. Period. This caused WH to mumble about "it's unfair" but I think it also gave him a jolt about how finances are about to be tighter.
Your wife is underestimating how much adulting she will have to do when the divorce happens. She thinks that things will be the same when that isn't the fact. She will have to kiss grad school goodbye as the child support won't cover everything nonetheless schooling. So be CALM. When she spews, validate but stay the course. Start agreeing with her when she talks about marriage not being possible, my DB coach recommended that and it had the desired effect. WH stopped using it as a way to instigate an argument. Can't exactly argue with someone agreeing with your point, kwim?
I can't remember which poster (I went through a lot of older threads when the signature line showed a successful DB) but his wife was having an affair and cake eating. At point she began to cross into physically attacking the LBS and was screaming she wanted a divorce. He agreed and then left, went dark for about 2 weeks. His WW ate her words and came crawling back.
Now, with that said, this does not always result in reconciliation. Sometimes the WS will make the same mistake over and over again, jumping from one relationship to the next to seek outward validation. There is something broke inside them and will not be fixed until they hit the bottom. So what you need to do is let go and let them fall, anything else delays the desired result. If you stick to your side of the road and make yourself a stud then you win no matter what the WS does. You exposed the affair and now you need to stop temp checking your WW. Get out of the house (for trips not move), take the kids if necessary, and go on trips, local fall festivals, whatever. She needs to be in the empty house and feel the absence. She can't miss you if your there in her presence all the time. Stop caring about what she says or threatens. If she files then do whatever necessary to speed the process. In the meantime, start grooming yourself, wearing some cologne, go out with friends and don't tell her who you're with. WS are weird, they don't want you until they think someone else does.
M 10yrs T 13yrs BD #1Oct 2015-PA between WAH and COW BD #2 April 2016-WH resumed PA, she broke it off Jan 2 2017 WH says he wants divorce April '17-Letting go 2018 D busted DD8, DS6, DS3