Isn't there something in the constitution about an unfettered right to earn a living and keep the product of ones labor?
Not in Family Court, there isn't. In fact, not only is there not a right to keep what you earn - you are be COMPELLED to pay, regardless of your actual income. (Well, not totally regardless - if your income goes up, you're supposed to pay more, but if it goes down, that's your own tough luck - you're supposed to find a job that pays more, not less.) You become an indentured servant to the ex in all but legal name.
1. Sell the house. It's hard, I know. You have to make your income cover two households' bills. You can't do that with the mortgage payment.
2. Live in a cheap apartment, whatever you can afford. The kids might have to sleep on the floor, or maybe you can find a cheap used pull-out couch. You might even have to bum room and couch space off relatives.
3. Tell her insurance company about her fraud. If it is at all legally possible, you must cut her off from the gravy train. The insurance company doesn't want to pay her to sit around and avoid work, any more than you want to.
4. Keep it in court. That's your only real hope to get anything changed. (Document - Litigate - Repeat)
5. If your choices are paying alimony or paying your bills, pay your bills. Living on the street won't help you any. Let her sue you for the back alimony. But continue to pay your court-ordered child support, and pay child support through the courts, NOT directly to her.
6. If the divorce is final, then the fact that she left you for someone else becomes irrelevant.