You would have got basis at the fair market value at date of death. Say FMV was $200,000. Then the gain would be calculated (Sales Price - $200,000 - Selling Cost).
If the transactions are closed, there is no way to structure a 1031 exchange. The problem with 1031 is that if you ever had access to the cash, you violated the rules of 1031. Therefore, it doesn't appear to be possible. See instructions for 1031 as follows: http://www.irs.gov/pub/irs-pdf/i8824.pdf
If you can substantiate either you or your brother living and owning in the property for 2 of the last 5 years, you may qualify for the $250,000 exclusion. If you or your brother can't meet this test but lived in the property for a while, there are some exceptions where you can prorate the $250,000 exclusion (such as health problems).
I would recommending, brainstorming to come up with as many additional expenses (flooring, plumbing, anything) you can associate with the property, include all escrow cost.
I don't believe there is anyway to invalidate the quick claim. You would need to consult with an attorney on this issue.