I would respectfully suggest you stop trying to arm-chair diagnose your WW and focus on things that are in your control - your WW's reasons and motivations have nothing to do with you at this point, and there is nothing you can do to change this.
What you can control is how this divorce is going to happen, and nothing will influence this more than your initial offer and moving out of the house.
Moving out and leaving her in the house with the kids is almost always a bad move. Unless you are in a no support situation (you make about the same or less than your wife, 50-50 on kids and everything else) then you moving out gives her a big advantage. By keeping the marital home, even if the time works out 50-50 it is generally presumed that she will receive support to maintain her lifestyle in the marital home. If she cant afford this on her own - you will have to pay up. Judges spend a lot of time considering the $ required to support the kids, they wont give a second thought about what you need to live on in your apartment, even if you have 50-50.
You need to force the sale of the house, hopefully before you move out. Once you are both out of the marital home and with 50-50, then you are on equal footing and there is no reason why you should have to pay more than temporary, rehabilitative support. Especially if you can work the ongoing affair into the conversation.
If you just have to leave due to the stress of the situation, then be very careful about writing terms for how long and under what conditions you pay support. I have seen exes live rent free for upwards of a decade by sabotaging sales and refusing to pay the mortgage, some even moving their APs in with them while the LBS foots the bill. You cant say things like "until sale of the house", you will need to say "for 12 months or until cohabitation" etc.
Your initial offer is the best that you will ever get. If you are paying up just to get out of the situation a few months faster, bear in mind that you will still be paying for this far into the future, when you will probably think of your ex as nothing more than a contemptible leach. You are so desperate to move out now that your instincts are to pay up and end the pain, but think about 5 years in the future and you are effectively paying for her cruise vacation with her boyfriend, just so that you could move out a few months sooner and try to avoid upsetting her.
Basically, what I am saying is that you need to tough it out now and stand up for yourself, because you are dangerously close to making some very long-term mistakes.
Finally, when you see a lawyer, expect realistic assessments that wont make you happy. But also expect to hear options and advice. If you arent hearing that, I highly suggest you consult a few more attorneys and see which ones are willing to go to bat for you.
