Well if it were me I'd kindly but firmly tell my wife that I don't want a divorce therefore I'm not going to make it happen or pay for it. If that's what she wants, then she needs to get a job and earn the money to do it herself, and that you'll comply legally when the time comes, but that in the meantime she can help get the bills caught up and don't put any further hardships on the kids.
In other words, be a leader in acting responsibly and rationally, not emotionally. But you have got to detach and put NO PRESSURE on her at all. Make living with you a joy instead of a burden. Be a great father and husband in everything while backing off the interpersonal stuff enough to make her comfortable. Spend time together as a family but don't manipulate or press her for alone time between you two.
You keep using that word. I do not think it means what you think it means. -- Inigo Montoya, 'The Princess Bride'