We build a lot of sidecar bikes for the R1200GS, Many are for dogs. For me this would be by far the best way to go. My own dog has been riding in sidecars for all of his 11 years and knows that it is his sidecar. If you are going to do any gravel roads it is a much nicer ride as the bike no longer falls over and as such you can pick up the pace a lot more then you would with out the sidecar. For your long trips, there is a lot more space to pack! Things that would be on your wish list to have with you no longer have to be as you have lots more space. Much better then putting your dogs behind you in a trailer with the exaust pipe aimed at them. The ride will be much nicer for both you and your wife with the sidecar as with out a passenger on the back of the bike there is more room for both you and your passenger to move around. My wife can also ride the GS which there is no way she could with out the sidecar as she would not be able to touch the ground. This works out good for pounding down the miles as we can trade off. Set up right, sidecars are a blast to ride, Set up wrong, they are anything but. Set up with an automotive wheel and tire on the rear of the bike you now have a 30-40,000 mile tire which if you are on the road for a couple of months is really nice. There is real good information on this site in the Hack'd section including photo's of our recent build of an R1200GSA with our M72DX sidecar and one of an F800GS with our M72D sidecar.
If you are not sure about sidecars, why not take a class? www.esc.org
sidecar bikes are provided. Adventure sidecar www.adventuresidecar.com
is also doing a "Tipi" tour which would give you a week or so on a rented sidecar bike along with sidecar training. If you are located any where near us I would be glad to take you and your wife out for a ride in a sidecar.