Yes, you can trade between family members with the Nintendo Switch version of Pokémon HOME.
Please keep in mind that some Pokémon, once moved to Pokémon Sword or Pokémon Shield, can’t be moved back to Pokémon: Let’s Go, Pikachu! or Pokémon: Let’s Go, Eevee!, even if the Pokémon was originally caught in those games.
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