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A couple of things to clarify the problem.
Although Stellarium shows sidereal motion in it's display it doesn't send tracking information to the mount. If you select an object in Stellarium you can (via Stellarium Scope) instruct the ASCOM (EQMOD) driver to tell the mount to slew to that object. It's only when you press a key combination (such as Ctrl-1) that Stellarium instructs the mount to slew. It will continuously read mount position and plot that in the display but will not send tracking information to the mount.
As you pointed out, EQMOD has various tracking rates including sidereal, lunar and solar and for DSO targets, sidereal is needed. Assuming you select sidereal and then start PHD2 guiding, PHD will not change the tracking rate but will instead make small adjustments (via ASCOM) to the RA and Dec positions to ensure your selected tracking star stays in the correct position of your guide camera and therefore your mount will accurately track your selected DSO. Obviously, if you are using PHD to follow a star (which must be moving at sidereal rate) it would make no sense to have your mount tracking at any rate other than sidereal.
You can effectively treat all of the programs as independent, all talking separately via ASCOM to the mount. Accurate goto in Stellarium depends on accurate polar alignment of the mount and accurate site location and date/time set in EQMOD and separately in Stellarium - usually supplemented by a star alignment routine with your mount's hand controller or with plate solving.
Kevin
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