Let's discuss Redemption:
Picard knew the Duras family to be treacherous and to be working with the romulans; if the Duras family would have won the civil war, the klingons and the romulans would have formed an alliance and come after the federation - which means bye bye federation.
On the other hand, Gowron was the legitimate leader of the klingon empire, recognised by the federation - which would make the Duras family little more than outlaws with a big gun.
So - the federation is both within the letter and spirit of any non-absurd law to help Gowron - unless helping another civilisation against terrorists/outlaws is also against the prime directive.
And the federation's prospects, indeed, its survival heavily depended upon the outcome of the civil war. Meaning, there's nothing sensible about the federation staying out of the civil war.
What does the federation do?
Invokes the prime directive to stay out of the war.
And the actions actually undertaken by Picard, far from being as efficient as advertised, should be useless. After the romulan warbirds were detected, Sela could have called Picard and demand of him to stop wasting her time; she has a civil war to win and afterwards, quite a few federation planets to burn. Followed by her continuing her supply run without using the cloak and the romulans openly helping the Duras family. You see, the fact that the federation proved the romulans were helping the Duras family is of no consequence; everyone in the Duras family already knew it and supported it.
But the writers needed a 'clean' solution, that respected the prime directive, regardless of its realism; and so the romulans inexplicably fled.
Another similar situation was presented in The circle (same type of order from the federation, but Sisko acted more sane).