How long ago was she ordered to do this---- ?
I think you have a problem but not an insurmountable problem .
"Wife shall take reasonable steps to refinance the home as soon as possible."
There may be some debate as to what that precisely means---but it sure reads like get it done soon---and you can ask court to determine what is "soon" --and I'd start by thinking 90-120 days is long enough to have moved it done absent impossibility.
My guess there are multiple such cases--people seem unwise in large numbers--so onecan probably do a data base search in you state as to what similar courts have held to be "reasonable" and what kind of cures were entertained.
To me a $16,000 refi cost is not impossible and if you can prove she got approved but turned down a refi you may be able to make her dance--court maynot be amused with her. And if she failed to make 3-4 application with correct data etc court may not be amused either.
You can always seek sanctions/costs-not sure if you'll get them..but if she comes in with an attitude of she won't refinance because of some cost which if not at all impossible the court could hold her in contempt or put her on an ultra short leash --odds are they will gicve her one more try --but unless you have good counsel and the one more try is very carefully worded as is the default step if she fails you'll be posting back here all to soon again.
You are probably lucky in a way--it seems she is able to refinance --the real problem is when folks are totally unable to get financing.
Lest your EX posture herself as unable to get financing--part of your preparation need to be to compel production of all the applications she made as well as her last several tax returns and anything else you counsel thinks might be useful relative to her ability to refinance or to discredit her with her own words. And me, I'd want tax returns and recent pay stubs for all adults residing at the home and name each of them
My guess is she is not about to refinance as she knows it grind you for her to not get it done and it probably gives her pleasure to know you are hanging in the wind as accountable to pay if she drops the ball.she gets a free ride on your credit.
Did you have counsel or did you do this financially unwise move all by yourself--I mean really-to give her the deed before she got it refinance is about as sophomoric as it gets . .