How much solar power is needed

To some extent it depends on the capacity of your battery. If you have sizeable battery capacity (more than 100ah) you might be able to get away with a 100w solar panel. But I would recommend getting a bigger panel (at least 160w) since you want to run your 2way fridge.

FYI, the factory installed Victron solar system puts out just under 200watts. There are several 200W solar "suitcases" out there that would likely be more than adequate for your purposes. 

Look for manufacturer and model number plate. A google search or perhaps someone on here can assist. It's likely a 12V/110V fridge that doesn't run on propane, but that's not a given. 

The above are all good suggestions / answers. But it will mis-lead you to either spend too much money for your needs or put the money in the wrong place. Not to scare you but for every system you need to watch your energy bank account. Every trip starts with a full charge on your battery.
1- you drive to a campground and hook into their power - you maintained your bank account and have enough power
2- you drive to a sunny open campground and position your trailer or solar panel to receive the sunlight
     a- Your bank account starts growing
     b- Turn on the high current refrigerator, your computer with the monitor 
     c-  Sun goes down, Your bank account is going down fast
     d- By morning your bank account (battery) was large enough to withstand the night's withdrawal and you leave to go home and recharge your account
3a- You live in the Pacific Northwest where the moss grows heavy for a reason and setup your trailer and solar panel to catch any available light
     a- Your bank account is savings only and doesn't grow
     b- Turn on your high current refrigerator .... and
     c- Next morning you're broke, the battery is dead and the breakfast meat is warm in the refrigerator
3b - You bought a Lithium battery! 
     a- You may have dodged the bullet today but it's a two day trip...
3c - You crank up the generator and supplement your account (battery) but you have to deal with the noise

There is no single answer. You need to know
1 - How much Energy (Amp * Hours) is available (stored) in your battery
2 - How much Energy you expect to use in 24 hours (1 day)
3 - How many days you need the above to last
4 - How do you replenish it or do you need to.

NOW you can ask about battery capacity, solar and or generator:

I - Solar is not an efficient way to replenish this energy but it's cheap (and quiet).
     a - Every AMP*Hour you have as a deficient must be replenished before you hit your battery's storage capacity.
     b - A 120 watt panel (for simplicity) produces 10 AMPS an hour but only when the sun is directly shining on it.  If in one day your deficient is 20 AMP*Hours then 2 hours will replenish your account or at least limit the deficient.
     c - The above may be enough if your trip is short or if the next day is much sunnier
II - Ultimately every dry camper must have a plan for their worst case trip
      a - That could involve a generator, large battery or a second solar panel for more efficient energy production
      b - Be aware of the current capacity and expected duration: battery monitor that includes a current "shunt". The monitor may be a meter (Victron BMV712 and others) or just the shunt but broadcasts to a smartphone the current energy accumulation (Victron Smartshunt).

Our "plan" is not in place yet as we are still learning but we expect a second portable array for spring / summer and move to a generator for winter and maybe fall use.

@Sharon_is_SAM
Good point...I was approaching this as since it seems he doesn't have factory solar he'd likely be going with a suitcase and the reference to the wattage was a guide when he considers which one to purchase. Price is of course a driver but on some models the delta between 130W and 200W is nominal. 

This forum is such an incredible resource. Even when posting in an effort to help others, one is also helped! That is a sign of a true forum family! 

Yes.

@Herg, you need a shorepower hookup or generator to run the air conditioner.  Having said that, if you have the stock battery with only about 75 amps and you plan on running the frig, pump and lights on battery (Friday on propane), a lot of owners get away with a portable 100 watt panel as long as you have a lot of sunlight.  You should take a look at the chart from jkjenn so you know what uses a lot of power - like the porch light, the light over the counter or the Fantastic fan at higher speeds.  Do you have a way to monitor your battery besides the SeeLevel?