Right inside the main panel where the Neutral and Ground Busses are bonded together, the voltage between the two (effectively across a short circuit) is near ZERO. HOWEVER as you get further from the panel and Neutrals and Grounds and Hots are all in paralell theres like a capacitor (capacitor effect) with possible voltage between two ends of a capacitor.
Similar, the voltage from Neutral to mother earth is near zero at the panel since the grounding electrode conductor (No 4 bare copper wire) is connected to the Neutral which leads to a grounding electrode (like a driven rod into earth). HOWEVER as you get downstream with Neutrals in paralell with hot conductors mutual inductance (transformer effect) plus the capacitance referred to above can all yield a Neutral voltage higher then mother earth.
Also old fashioned analog meters and newer digital meters yield different results subject to their input impedance and how they work, I love my old Simpson 260 analog in these applications. An "ideal" voltmeter has INFINITE resistance so it doesnt draw current and affect the true voltage between the test points.
Sure the 3 way switch (two single pole double throw switches) is wirede correct???