You want to sell the house as soon as possible so that you can still qualify for the home owner exemption exclusion of 250,000 for the two out of the five years. The below citation and website links to the IRS websites are for your further reference. If you loose part of the two years because you had to move for the military duty, you may be able to still qualify for the exemption.
You will have to separate the rental part from the primary home residence part. The part of long term capital gain from adding back the depreciation has to be used for the rental part, that is, you need to report long-term capital gain if the rental part has a profit due to the adding back of depreciation taken. The adding back depreciation cannot be covered by the 250,000 exemption.
The below IRS websites and links are right on the point for your situation.
If you permanently moved out of Colorado, you should have reported rental income in Colorado. So, follow up with that tax return to file a last year tax return on the rental property and report the sales gain in the state of Colorado as Colorado income.
The sale of the property is reported on the Form 1040 federal return and also flow to your Tennessee tax return as how you have reported the rental income as in the previous year. The State of Tennessee should give you credit for income tax paid to Colorado for the sales profit.
Please feel free to follow up.
Fiona Chen, MPA, Ph.D., CPA, ABV, CFF, CITP
"To exclude gain, a taxpayer must both own and use the home as a principal residence for two of the five years before the sale."
Example, "Amy can exclude gain up to $250,000. However, she cannot exclude the part of the gain equal to the depreciation she claimed for renting the house."