All the grounds tie together. Keep in mind that a 2000 watt inverter can only supply about 15-16 amps. A #14 wire can carry that much so your concerns about overloading a neutral are unfounded. However, feeding half of your breaker panel is not necessarily wise. That is why most times the inverter has a separate feed from a 20 amp breaker in the panel, and the output from the inverter is fed to a "sub" panel. Keep in mind that your original panel is also a "sub" panel, meaning the ground and neutral are NOT bonded together in your panel because the ONLY permitted bond occurs at the campground service panel. Hope this helps.
