I don't agree that her name being on the deed automatically qualifies her for half the equity, especially if he owned the home prior. A court might just award her a percentage of the increase in value during the marriage.
That $31,000 equity will disappear very quickly when you factor in at least 4% sales commission to the broker = $6000 and closing costs which may not be much for the seller but could still be a few thousand dollars so figure another $5000 anyway so that $31,000 is now $20,000 and the odds are the house won't sell for as much as you think it's worth because, well let's face it we all tend to overestimate the value of our assets.
So when it comes right down to it there isn't much equity in the house -if any- and you could even be underwater if the mortgage is in fact more than what the house will sell for.
Either way if you want to stay and she wants out, it all comes down to what she's willing to accept for her half of the equity, which, as I just calculated above, isn't all that much. If you could get away with offering her $10,000 to walk away from the house you'd probably be doing ok.
I agree, adding that it depends entirely on what state you live in plus which judge you get.
You can claim your downpayment as a prior asset. Browser is 100% accurate about calculating equity. You take the appraised value and subtract out the costs to sell. Then subtract what is still owed on the mortgage. This is the true equity in the home. You subtract your downpayment. Divide that by 2. This is the amount of money she is entitled to out of the house.
You might even be able to argue she is only entitled to half the increase in value of the home, but this depends on where you live. Putting her on the title to the house may have given her half the total equity, but it may not. It depends on your laws and courts.
You should file for the divorce rather than waiting for her to file. If she files first it isn't the end of the world but you do lose some potential psychological advantage. Anyhow, in the filing you put all the details including what you claim to be the equity in the home and how much goes to her. She of course files her claim which will probably be different than yours.
In terms of forcing you to sell, no she can't do that. She can ask to keep the house and buy out your half. Or, she can ask for $$ for her half of the value. In the first case you might be fighting with her about who gets to keep the house if you want it, too. That's what lawyers and mediators get paid for, to figure out which way to settle the argument. In the second case the court won't care how you come up with the $$, whether you sell the house or keep the house, just as long as she gets her $$.
Also, the settlement is a bottom line number. You add up all the assets, subtract all the debts, and divide by 2. That is the $$ you are each entitled to. (This is simplified, as you each keep stuff you brought into the marriage, and other special exceptions). You can take your half any way you can get an agreement on. For example, you can keep the house and she gets the cars and furniture. As long as the value of what you get is the number that is agreed upon, you can split the objects and bank accounts any way that works.
She can't force you to sell but she does get her $$.