There's no "strategy." The old rule to postpone gain by purchasing a new home was eliminated in 1997. Each transaction is treated on its own.
1. Mountain home bought 1994, lived until 2/19, sold 5/21.
You qualify to exclude up to $250,000 (or $500,000 if married filing jointly) of your capital gains, and will pay long term capital gains on the rest. If you were carrying forward a capital gain in 1994 (from the old rule) then you must reduce your cost basis for calculating the gain. You must also reduce your basis (depreciation recapture) by the depreciation you claimed or could have claimed while renting the mountain home. You can also reduce your gain if you can document increases to your cost basis like certain closing costs and improvements. See page 8 of publication 523.
https://www.irs.gov/pub/irs-pdf/p523.pdf
2. Hemlock purchased 2/19, sold 9/21.
You also qualify to exclude your gain on this home, assuming you lived in the home as your main home for at least 2 years (731 days, do not have to be consecutive). However, you can only use your gains exclusion once every two years, so you will have to decide whether to use your exclusion on the Hemlock house or the Mountain house, and pay the full capital gains tax on the other. (Generally, use the exclusion on the home with the larger gain, of course.)
3. Curtis, bought 6/21 and rented out.
4. Carla, purchased 8/21
Irrelevant, neither of these situations affects the tax on the sale of the Mountain or Hemlock home.
