My opinion:
First of all, you shouldn't be quitting your job just so you can take care of the kids. You should keep your current job and make HER work it out (or at the very least, both of you keep your jobs and find a way to make it work) so that the kids are taken care of. It's no fair to drop this piece of shit bombshell on you and expect to have you take care of everything while she's at her sister’s house doing nothing and going out every other night after school while she knows that the kids are being conveniently taken care of. I think that she doesn't want to do the work. Maybe she really is burnt out too. I don't really have enough info to determine that. I kind of went through the same thing with my wife. She snapped in a very similar way like yours did. I really don't know what the fuck happened to make her snap like that but it all started when I hung up her clothes in the wrong direction in the closet (yes her clothes has to face a certain way when they're hung up in the closet or I'm not "respecting her needs." Women...
) after doing laundry before I went out of town for my job at the time. So I kind of know what you're going through, but without kids being involved.
I don't know about her fucking around on you, she might be, I'd just be on the lookout for warning signs. And not knowing your wife, I really can’t say what those are. Only you'd be able to determine that. Maybe she feels that she missed out on her "youth" and wasn't able to fuck everything in sight. Personally, sometimes I feel the same way your wife does. I didn't go out fucking everything in sight and I got married at 20. I'd be lying through my ass if I said it's been easy for the last 8 years we've been together. But I know one thing, her saying that she wouldn't fight for her marriage isn't a good sign. But you already knew that. Don't know if this helped you or not but at least know that you aren't alone.