Normally, since you have an agreement there would be little you could do. But if you can show that he has voluntarily reduced his income and is knowingly putting the mortgage in danger of foreclosure the courts could force him to uphold the agreement that he signed in the beginning or come up with a new amount.
My suggestion would be that the home is refinanced to get his name removed and you file for alimony so that the money is paid to you instead of paying the mortgage. This at least will get his name off the home and will mean that he no longer has control of your credit…but it will also mean that you will be responsible for the payment regardless of whether or not he pays you.
He can reduce his annual income, but if you can show that his income reduction was voluntary, then the courts could force him to pay the previous amount based on salary potential.
As far as the children go…I will only say this. If he has proposed to this woman then she is going to be in his life. I suggest that you have a talk with the children about this. Get a working visitation schedule and stick to it. This is their father and they legally have no say in this at the moment. NC prefers that each parent be as involved with their child as possible and will default to joint legal custody if custody is not agreed on or determined in court. They may not see it now, but they need to have time with their father. They need to have time to get to know this woman and her children if they are going to be related to them. My suggestion is that you talk to your ex about this. This is not about you or him, it’s about the children and what’s best for them.