The Prime Directive restricts Starfleet's options in first contact situations, yes. But it also restricts Starfleet's options in later dealings: it was explicitly quoted as the reason Starfleet couldn't interfere with Bajor's civil war at the start of the second season of DS9, and as the reason Starfleet couldn't interfere with the internal politics of Angel One, a well-known world, in the titular TNG episode. It was also associated with Starfleet's staying out of the Klingon civil war.
It should be pointed out, though, that the PD only restricts Starfleet. It has never been explicated as a limiter of Federation policy except when it comes to executing that policy through Starfleet. Indeed, the only time it has been applied to an apparent civilian (in the sense of limiting the options of that civilian, not in the sense of protecting the civilian from Starfleet action) is in "Bread and Circuses", where the commanding officer of SS Beagle
was to be dragged away in chains for violating it. But the status of said officer as a "civilian" might be disputed...
So the UFP government may practice all sorts of realpolitik regardless of the PD. Indeed, the UFP government is the one organization empowered to alter the PD to meet the requirements of the day. The PD just keeps the soldiers of the Federation from meddling in politics.
We do know that Kesprytt was considered for membership despite having a territory that wasn't part of the unified global government, but likely due to the events of the episode their membership was rejected.
So in theory, split planets are quite eligible; in practice, it's just not done, especially if the first serious attempt at it ends badly.