IIT,
For the moment, I think it is best that you say as little as possible to your wife about anything relating to the marriage or separation. And do not let her push your buttons on this. She sounds like she enjoys being nasty, so prepare yourself for her attempts to goad you and manipulate you by practicing a stock response of, "I am not discussing that."
If she asks why you haven't moved out, tell her the ultimatum was a test, and you got the information you were expecting. She is clearly a liar and a manipulator, so why should you stick by anything that you say in relation to her? Particularly if it is going to make your life harder. If you have nowhere to go, stay where you are.
If you leave, and are gone for a couple of weeks, a person like her is likely to try and shaft you for "abandonment", even though she abandoned you and the family for more than two years with her relationship with the 'friend'. Do not give her any ammunition, IIT.
Do get yourself another VAR to keep with you, and use it if she starts getting vindictive with you, or if she wants to discuss anything 'serious' relating to the marriage. Do not underestimate how low she will go.
I know your world must feel like it is rocking off its hinges at the moment, but stop for a moment, take a deep breath, and think:
Neither of you have taken any official legal action, so in the eyes of the world and the courts, you are a married couple with four kids, living in the family home. As unpleasant as your wife has become, the set-up is actually good for you, because YOU DO NOT HAVE TO CHANGE A THING FOR THE NEXT THIRTY YEARS. I say that with particular emphasis in relation to you packing your bags with nowhere to go. DO NOT DO IT; YOU DON'T HAVE TO GO, SO STAND YOUR GROUND AND STAY.
If you end up homeless on the streets, that delightful creature you are married to will sit back and laugh, as she sits on her ass in the home you paid for. WHY GIVE HER THAT SATISFACTION? You paid for the place, you stay in it.
If you pack up and leave, you make life very easy for her. Make it harder for her and stay. If she wants you out, let her find the money to take legal action to evict her husband from the family home. See how far she gets with that! If she wants a divorce, let her save up her money from her lazy-ass part-time job and pay for the lawyers. Again, see how far she gets with that.
And seriously, where does she think her life is going? Some fantasy la-la land where she marries her friend, and lives happily ever after? Well, for that to happen, there would have to be a divorce, and if there has to be a divorce, YOU MAKE THOSE TWO DELIGHTFUL PEOPLE PAY FOR IT. They want to play, make them pay. Do not start any legal action on your dime, or you will end up paying for the divorce that they use to get together.
With household bills, you ratchet back and start paying half, and she pays half. If she can't afford that, she'll have to stop spending her day on the phone and start paying her way. If she doesn't want to do that, she'll have to tighten her belt. If you pay her phone bill, stop immediately. If you pay any kind of insurance on her, stop immediately. Pay for yourself, make sure the kids are okay, but you make her start paying her way. She thinks she can do without you? Fine. Put the phone down and start working, peaches!
You see, where you feel all is lost, and she is somehow in charge, the opposite is actually true. You are the major breadwinner, she depends on you, and in the eyes of the law, you have every right under the sun to remain in that house, with your kids, for as long as you want to. Once you cut back on the money, what is she going to do? Beg from her family or her 'friend'? Fine, let them pay for her lazy, selfish lifestyle. You won't be, and that will be good for you.
The money you save by not supporting her can be stockpiled for you, for the future.
Seriously, IIT, as horrible as your wife's actions are, you must put any plans of moving out on hold. Put everything on hold, get yourself together, and think about what is best for you and the kids on a day-to-day basis for the immediate future. And I promise you, staying put is much better than living in your car.