How you use the proceeds or when you buy a new home is irrelevant, each sale is treated as its own separate event. (Rules related to postponing gain by buying a replacement home were removed from the tax law in 1997).
All the rules on the current exclusion are covered in IRS publication 523. In particular, you may qualify for a partial exclusion if you sell before 2 years due to certain financial hardships, as listed in the publication. If there was no hardship and it was just your choice to move someplace different, then you can't use the capital gains exclusion.
https://www.irs.gov/forms-pubs/about-publication-523
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