Hi, I'm Heather, a family law attorney with 15 years experience, and I'd like to assist for informational and educational purposes.
I spent a bit of time reading that document that you attached. The answer to your question is going to turn on exactly how the judge interprets that decree/contract language. I think that if you study the language for a bit, it actually appears that he cannot demand the appraisal if you already have the house for sale at its fair market value. The language clearly states that if you are selling the house, YOU list the house at fair market value, and YOU determine the final sales price.
The part of the provision that discusses the appraisal applies if you DO NOT want to sell the house, but rather simply want to pay him his share of equity from the house.
While it may be good of you to let him get an appraisal if he wants to pay for one, and let him show it to you if he wants to do that, and you can certainly consider it when setting the listing price (and you should consider his appraisal if he gets one, because that will be relevant on what the fair market value is), the provisions are pretty clear that if the home actually is listed for sale, then you list it, you sell it for fair market value, and you have final determination over the sale's price.
Has that helped? Please let me know if this answered your question and thank you for using justanswer.com!