You can deduct the interest on a construction loan is if it was a mortgage as long as you finish construction and get a certificate of occupancy and move in within two years of opening the construction loan.
As long as the home has been your main residence for at least the past two years, and you sell it within two years of beginning renovations, you will be able to exclude the first $250,000 of capital gains from taxation, or $500,000 if married filing jointly. You would get the same exclusion if you sold the home as is, of course. To calculate the adjusted cost basis, you could include all of the costs you pay for labor and materials for the renovation, but you cannot include any cost basis adjustment for work you perform your self that you don’t pay for it.
Whether it is a better investment to spend a great deal of money to rebuild the home and sell it, over selling it as is for less money but without the added cost, is something that would require a great deal of financial expertise to analyze.
The only elements that would impact your income taxes would be the requirement to complete the renovations and close on the sale within two years or less of the day you move out of the home and start living someplace else. (Both for the mortgage interest deduction and for the capital gains exclusion), and a requirement to keep track of all of your renovation costs.
