Damn, I am sorry to read this. As so many have testified in this thread, you aren't the first to have it happen, but it still hurts intensely personally.
So, mostly my advice echoes what's been offered:
1. Lawyer
2. Freeze assets
3. If you can stand the loss, cut your material losses and let her have it. Eventually, you will get new stuff and she'll have the by now old stuff that breaks and is utterly not your problem.
4. Lawyer for any communication if at all possible. Even if this is "amicable," using a lawyer can help prevent another last minute surprise as like what set this sad thing in motion.
5. If you can afford it, and this sounds like the absolute worse time for it - starting airline pay, temp Guard time, etc., offer big on child support in return for reduced or no spousal support. She can get a job as her newly acquired license shows. And if she does become successful, there's nothing that prevents you from seeking spousal support in a community property state. 'Sacrificing' now for and with the kids will eventually end and you are shed of her and any further commitments to, for, and around her. Free at last, free at last, thank God almighty, you'll be free at last.
6. If possible, I might disagree with the staying in the house stand. Too much opportunity for her to say you lost your temper and she needs more compensation. If you aren't there, and you both are gonna have to sell the house anyway (1/2 the sales cost is on her, btw), it doesn't really matter. And keeps you in the use a lawyer for any communication mode.
That 1/2 of all bills/expenses from her execution day forward should be split in a community property state (Ask me how I know...). That's a fact that she may not be expecting; some substantial debt starting now vs. the pay-off she might've expected.
That's leverage for you - "I'll take X amount of debt now in return for no/smaller percentage of spousal support." Again, some pain and money out of pocket now and a cauterizing of the financial/emotional wound fairly soon.