Your inverter should be mounted as close to the batteries as practicable and in a dry spot. Mine is in the cave, and not connected to the DC distribution panel. You're correct that the cable to the DC distribution panel may not handle the added load. There should be separate cables, either from the battery buses or the batteries directly to the inverter. I think the manual also calls for a fuse, and an on/off switch is a good idea, too. The total length of the positive cable for the DC portion of the system can be less than six feet if you mount the inverter in the cave.
As far as the AC side of the system, you have choices. The Xantrex inverter has an AC outlet directly on the unit. If you use this outlet, you don't need to do anything further. Just plug your appliances into the outlet on the inverter. If you want to use the outlets already built into the boat, you'll need to connect the inverter using a separate, grounded AC cable from the inverter to the AC distribution panel. Presuming that you don't have a generator, you can use this empty space on the panel. There is a slide on the panel to prevent you from using both the inverter and shore power at the same time. You just turn on either the shore power switch or the generator (inverter in your case) switch, and that will connect your inverter to the AC system of the boat. You can then turn on the switches for the outlets (dining area, galley area, etc.) and use them as though you were plugged into shore power.
I suggest that you hire an electrician if you're not sure how to make the various connections properly or calculate the cable sizes required for your particular installation.