Quite a few issues but here goes!
The last thing you want on the flightdeck is an argument! If what is being done is safe notwithstanding that you have drawn attention to the fact that it is not in accordance with SOPS then I feel you have as the second in command done your job. If its not safe that is a different matter!
Its surely not so much a question of what so and so told you to do but what the operations manual for your company states. I like the phrase "Documentation beats Conversation" - consulting the manuals is professional and takes away the personality aspect! Remember dont shoot the messenger, even trainers are human and sometimes dont get it right!
Maintain good relationships with whoever you are flying with and dont get into the us and them syndrome!