3 domains, 1 wordpress install, redirecting and changing domains on live site

It’s still confusing a little bit but definitely not best to resolve this with WordPress.

Many hosting providers offer you to set domain redirect right in their control panel and often that’s the easiest to manage and also not require you to have web hosting with them (domain control is enough).

If I understand your situation correctly, you want to:

  1. Redirect Domain-A to Domain-C
  2. Redirect Domain-B to Domain-C
  3. Set A record (IP address) of Domain-C to Hosting provider #1