Seek legal advice. Do not let her bully you into anything. As I remember you were given advice to return to your marital home and after legal advice you decided not to. That is OK, but time for your A-game. It is apparent to me, she wants to bully you into moving out (which you have), keep paying the expenses and basically enabling her. Again, seek legal advice. Instruct the lawyer to come up with a bulletproof plan for you to remain in your home with the children, and if she wishes to leave, she can do so. I feel for you buddy, this really does suck. At BD, my kids were 2 and 5 (now 6 and 9) so I can only imagine the turmoil.
This situation that was thrust upon you will take all your strength to navigate.
Please bite your tongue and do not even raise your voice against your W, record all your interactions and better yet, have a witness present at interactions. IMO you have to establish a foothold somewhere and anchor your ship there. You have to remember she is no more a parent than you and your rights as a father matter just as much.
Regarding your last question, what would it solve if you filed first? What tactical advantage would it bring you? If you are counting on you filing shaking her to reality, forget it. IMO you are only trying to illicit a reaction. This will do you no good.
