it prohibits interferences in the internal affairs of any society. Even if they're your biggest ally asking for help in a civil war that was instigated and supported by your biggest rival.
GOWRON: ... request your assistance in fighting these enemies of the Empire.
RIKER: These enemies are Klingons.
PICARD: ... by definition, an internal Klingon affair.
(and)
ADMIRAL SHANTHI: The Klingon civil war is, by definition, an internal matter of the Empire.
PICARD: Agreed.
I don't think that the prime directive was in play in Redemption. The noninterference referred to in Redemption had to do with the separate issue of interfering with another sovereign power. Not all "noninterference" matters pertain to the prime directive.
And in the case of Redemption, once it became established (and not just supposed) that the Romulans were involved, the Klingon government was able to invoke a existing mutual defense treaty with the Federation.
