What you've described does not make sense, based on the diagram shown. The volume and tone pots should function normally. If they don't, you have not followed the wiring properly, and should double check it.
There are two issues with your diagram, though. First off, there is no need to ever switch grounds. You want everything operating at the same ground potential, regardless of the switching, in this instance. Second, you have the volume pots wired with the wiper terminals varying output impedance at the jack, but there is no pickup selector to allow for pickup soloing. Rolling either volume down will kill the output, so there is no way to solo the pickups unless you swap the terminals around to allow the resistance of the volume pots to vary against the pickups while the output impedance remains constant for the other pickup when soloing.
Also, there is no need to even have a switch in the circuit. You can do mono/stereo switching with the proper choice of jacks, so that a cable in the stereo jack carries two signals, while a cable in the mono jack shunts the two signals to one output when needed.