A second home is a capital asset. It does not get the benefit of a exclusion like a primary residence or the ability to generate a loss like a rental property. It is the straight-forward sale of the asset.
The gain is determined by the difference between purchase price plus improvements and the sales price. The mortgages have nothing to do with the sale reported to the IRS. You took out a loan and used the money for some purpose and now you have to pay the loan back. A mortgage is backed up by the property, but it is still just a loan. In the example you gave above, your gain would be $200,000.
