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.
You continue to grossly misinterpret the Prime Directive. It was precisely outside interference on the part of a rival power that enabled Picard to take action. While it was an internal matter, it was very sensible not to get involved...that sort of thing is the "no-brainer" excuse for having something like a Prime Directive. But the Prime Directive doesn't prevent the Federation from protecting its interests from enemy actions, particularly when those actions involve the Romulans breaking treaties with the Federaton (crossing the Neutral Zone).
Protecting the Gowron regime from an internal uprising was something that the Federation didn't want to get involved in. Protecting it from a Romulan invasion was.
You like to imagine an extreme interpretation of the PD that obviously wasn't exercised in the examples that you cite.