•You are a sole or joint owner.
•Your spouse or former spouse is allowed to live in it
under a divorce or separation agreement.
•Your spouse or former spouse uses it as his or her
residence (not just as a second home).
So if your ex-spouse used the home as their primary residence and is allowed to exclude their gain, you can exclude your gain as well. You can exclude up to $250,000 from taxes. Gain more than $250,000 will be taxed as long term capital gains.
Note that your gain is not the amount of cash you received. Your gain is the difference between the selling price and the cost basis. (For example, if you purchased for $100,000 and sold for $300,000, but only received $50,000 due to an outstanding home equity loan, your gain is still $200,000.) In your case, if you are due (let's say) 33% of the proceeds, then your gain is 33% of the sales price minus 33% of your cost basis.
The selling price for tax purposes is the actual contract selling price minus certain expenses of selling (real estate commission, required inspections, taxes and fees you pay for, and buyer's closing costs if you pay them for the buyer). You can't subtract cleaning or staging costs. The cost basis for tax purposes is the original purchase price, plus original closing costs like inspections and bank and attorney fees, plus the cost of any permanent improvements you made to the property.
If your gain (after the above calculations) is less than $250,000, and you meet the tests at the top of the question, then you don't owe tax on the sale. You don't even have to report it on your tax return, unless you or your ex received a form 1099-S at the closing. If you got a 1099-S, then you have to report the sale even though it is tax-free.
