We sold our second home (non-rental) this tax year and netted $186K and reinvested it in another home the same day. How do I report this without capital gains tax?

You can't. If you have a gain on your home, it is fully taxable. Back in the 1990s, if you bought a more expensive home, you could defer gain but that law is long gone.

A personal primary home could qualify for an exclusion but a second home doesn't.