Also, Satie outranked Picard, he couldn't have thrown her in the brig.
If Starfleet is similar to the US Navy (as I and others believe), Captain Picard actually could have placed Admiral Satie in confinement. Her being of superior rank wouldn't have stopped that all by itself. If her offense warrented the brig, then she would have been placed there.
True, more likely her confinement would have been in her quarters with communications and computer access restricted. But if she refused to co-operate, then throwing Satie into the brig wouldn't have been out of the question.
RHIP only goes so far.
on whose authority or what charge would be confining her on? The investigation she was conducting was authorized.