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.
Except it wasn't the Duras family fighting chancellor Gowron. It was the Duras family's coalition fighting Gowron's loyalist coalition. Once the Duras sister's connection to the Romulans was confirned, the Duras sisters no longer possessed a coalition. Their support among their former allies disappeared. The allies would switch over to Gowron, or simply stand to the side.
Why would the Romulans continue to aid one
That the others in the Duras coalition did not know about the romulan help is unsupported - and not really plausible:
Unless all in the Duras coalition except the Duras were fools, they already knew they were receiving outside help from the romulans - the supplies were on a massive scale, providing the necessary provisions for entire sectors.
My read is that it wasn't the PD that kept the federation out of (what they thought) was purely a Klingon civil war, but rather "non-interference" in a foreign cultures private matter. Once it was confirmed that it wasn't internal, a standing mutual defense treaty came into play.
PD with different (but nevertheless quite similar - non-interference taken to the extreme) provisions for pre and post warp societies or PD and another law - same difference.
Also, as per this PD for post warp cultures:
If the Duras were seen as outlaws/terrorists, the federation should have intervened from the start (assuming a sane PD).
If the federation recognised the Duras some legitimacy, it could not intervene regardless of whether the Duras asked and received help from someone else (including the romulans); in this case, it's their business whom they ask and receive help from.