A more common approach is to use a transfer switch to shift between power
sources.

As installed, the power mains are the primary supply and, when they fail or
are otherwise disconnected, the backup power source takes over. This backup
source may be a generator, solar, batteries, or wind.

A Transfer Switch is far less expensive than duplicate wiring. <G>

Hi,
The best way to go would be a 2000W inverter/charger (Heart Interface,
Xantrex now, is what I have) coupled to an automatic change over switch
for using a generator or when connected to shore power.   When using the
batteries only the inverter section of the inverter/charger would be
supplying power from the batteries for any AC items you might have
connected to it.  When hooked up to shore power through an automatic
change over switch the charger section of the inverter/charger would
charge and maintain your batteries whenever you plugged into AC shore
power.   Good inverter/chargers would supply 3 stage charging keeping
your batteries in top condition.  A good control panel like a Link 1000
should be used in combination with the inverter/charger.  You might want
to look here to see what I'm talking about.  Note that even though these
inverter chargers have a built in transfer switch you still need an
automatic switch if you plan on using a generator, or at the very least
a cable and plug.
http://www.xantrex.com/web/id/49/p/1/pt/24/product.asp

The solar panel and charge controller would be hooked up to the
batteries and supply a charge to them when the panel was in sun light.
The charge controller would determine how much of a charge to supply
from the solar panel, a C12 controller is a good choice for panels
supplying less then 12 amps.   The charge controller along with the Link
1000 or other inverter/charger control panel would need to be set up to
prevent overcharging of the batteries.

The above system is basically what is used on most newer RV's that have
large inverter/chargers.

I don't know why you would need to disconnect the batteries from each
other to charge them.  If you are going to use them with a 2000 watt
inverter you will need heavy cables between the batteries and the
inverter.  These cables will be more then capable of handling any
charging currents.  The batteries and inverter should be as close
together as possible.  The shorter the cable runs the better.

There are other ways to do what you want using a plain 2000 watt
inverter a 3 stage battery charger and change over switch, but the basic
setup would be the same.  Batteries supplying power to the inverter, an
AC battery charger hooked up to the batteries to charge them when on
shore power, and a change over switch to take the inverter out of the
system when hooked up to shore power.  The change over switch can be as
simple as a plug as long as you NEVER forget to use it.

Hope this helps some.

Others have mentioned the transfer switch.  On my rig there is no
transfer switch.  The output of my generator goes to an outlet.  I
plug my shorepower cable in to the parks pedestal when available or
into the the genny outlet.  No reason your invertor couldn't have an
outlet that your shorepower cable can plug into.

Jon