A decree of divorce is a court order. Full and voluntary compliance is expected by all parties. It is enforceable through the contempt powers of the court, which involves punishment by incarceration. Because impossibility is a valid defense to contempt, it is unlikely the court would assess jail time for not refinancing, but there is considerable exposure to punishment for contempt for not selling. It is irrelevant that it "would devastate my kids." A different arrangement will be available only if the ex agrees to it. Because the liability of the ex on the current mortgage may make it impossible to buy a new home, discharge of liability on your mortgage is a big issue, and refusal to extend the time for resolution is not an unreasonable or unexpected response.
Best wishes for an outcome you can accept, and please remember to designate a best answer.
This answer is offered as a public service for general information only and may not be relied upon as legal advice.
In order to answer your question fully or specifically, I'd need to review your separation agreement and especially the provision to which you refer. The language is important. However, your ex might have grounds to file a Motion for Contempt if you do not comply with the court's order.
Generally speaking, a finding of contempt requires the court to find that you have willfully disobeyed or disregarded the court's order. Making your best effort to comply is necessary so that you can present to the court your defense if you should be called to court on a Contempt Motion.
Therefore, I suggest that you (1) make your best efforts to refinance the mortgage, even if it results in a denial of your refinance application. It is important to show that you've made a good faith effort to comply with the court's order.
(2) I also suggest that you obtain a written fair market analysis of your home from a real estate agent .
Depending on the results, you and your ex [and/or the judge] may consider it important information in deciding whether or when to list the home for sale if a refinance in your own name isn't possible by the end of 2013.
You could consider whether it is appropriate to file a Motion to Modify the provision requiring your refinance or sale of the home using the denied refinance application and fair market value analysis to give you more time to improve your employment status so that you could succeed in a refinance. It might especially be helpful if the refinance application denial indicated that the basis for denial was your inadequate income if you have some reasonable expectation that you will soon have adequate income because of a change in your employment, raise, or other anticipated increase in income.
Finally, have you discussed this with your ex lately? It may be that he'd agree it is in the best interests your children that you remain in the house until the present school year ends and then either successfully refinance in your name, or sell.
In my opinion, agreement between the two of you is the best way to achieve not only the best results, but also what is in your children's best interests. If you do come to an agreement between the two of you to extend the refinance or sell deadline until the end of the 2013-2014 school year, you could put that agreement into writing and submit it to court as an agreed modification to the present provision directing you to refinance or sell by the end of 2013. That way, this new deadline could become the order of the court.
These are just some ideas for you to consider. I recommend that you consult with an attorney who can review your Separation Agreement, discuss with you the specifics of your personal particular situation, and possibly help you and your ex reach an agreement on the issue without the need to involve the court on a Contempt Motion.