Hello Nancy -- and a hearty welcome to the Forums! Going green is an admirable direction (this coming from an active Sierra Club outings leader). Another interest you may have is extending your boondocking ability.
Wattage ends up setting an upper limit to what solar can do. Due to the limited roof area on any Airstream, some people try solar panels on some sort of stand or tripod set on the ground at the campsite. Adding panel area adds costs quickly. One can discuss shady campsites vs open areas (more common out west). But the real limit ends up being how many pounds of batteries you can carry. There's not an Airstream made that will carry the load of enough batteries. It is fair to say that reliance on solar will not allow any A/C or microwave oven use. Even the installed one or two batteries on current Airstreams take a surprisingly long time to recharge when hooked up behind a running tow vehicle -- maybe 2-300 miles! Also note that battery life is best when not discharged much below halfway.
2-way (LP & 110V) fridges are the most common installation in RVs today. 3-way (LP, 110V & 12V) fridges aren't frequently installed. This makes sense when one looks at availability and economy of LP. Two 30 pound cylinders will last about the entire camping season for me. More info could be sought if you wish to pursue the 12V fridge idea.
questions tend to bring analysis compared to a generator
. I would do a search on both those words. Small generators may also not be able to run the A/C but they are quiet and can help with mealtime or microwave power requirements. Some people have even converted their generators to LP use so that they don't have to carry containers of gasoline in their tow vehicle.
[on Edit] Oh yeah... I did overlook the point that a 3-way fridge does allow non-LP refrigeration while underway, therefore you can turn off the LP valves. This is a safety measure that many swear by -- and just as many run with their fridge on LP anyway (I am usually in the latter category). It is advisable to turn off your fridge before you near gas pumps when fueling a gasoline powered tow vehicle.
OEM installed electric systems in tow vehicles provide a minimum recharging ability when a lot of accessories are turned on (headlights, A/C, etc). Heavy duty alternators do make more sense if you have a choice. Unnecessary for my use, my truck is equipped with a snowplow package -- heavy duty alternator + 2 batteries.