Something doesn't sound quite right w/your situation. I'm not sure you have a clear understanding of the facts of your situation, but I'll try to give you the best answer I can with the details you provided.
You say you are divorced, but you are citing a separation agreement.
So, are you separated or divorced?
If you are divorced, then your previous separation agreement is meaningless.
You might, however, have a SETTLEMENT agreement that would carry weight.
Having someone make half the mortgage payments on a home she no longer lives in for an unspecified period of time is highly unusual, and I wonder if that is really what the divorce called for.
Whether she is entitled to equity depends on your final divorce paperwork. If it says she gets half, then she does, according to the terms of your papers. If the papers do NOT address that specifically, then my guess is that it's all yours.
If you had an attorney represent you, go back to that person and get some clarification on this.
If you did it yourself, ay caramba.
If you want to protect your credit, you will have to pay her shortfall on the mortgage. Period.
The bank doesn't care who is "supposed" to be making the payments, according to the terms of the divorce. If the payments are late or are short, it WILL be reported on both of your credit reports.