Well. Speaking from experience on this
When I pulled a trailer one of the campgrounds I visited regularly (My favorite iun fact) started charging for electricty.. I had been buying ICE, lots of it some months, for the Coolers but since they were charging for Power.. I went to SEARS and came home with a big box (Dorm/office size fridge, or "mini") same as you have, 100 watts it said on the ID label, but a 450 Watt inverter would not kick start it. I now have a 750 that might (I think) but alas, no longer have the fridge, a 1,000 DID (Ok so that was a Genrac Generator). with power left over.
Connecting the inverter to the Battery......
When you break 100 watts you need Big Heavy Wires.. Most of the wiring in an RV can handle 100-200 watts but the voltage drop may cause the inverter to crash (Error out) over 100 watts... 500 watts or more is a serious overload on the existing wiring.
How to fix
Get ye to Auto-Zone, Discount Auto, Store AUTO dept, NAPA, ____ Auto Parts (you fill iun the blank)
And pick up the following
One short RED starter cable
one "T" Fuse and holder, size depends on inverter, about 11 or 12 amps per 100 watts is a good guide line.. Or if the inverter has a DC fuse get the next size up.
A longer RED starter cable
And a BLACK cable
How long the long cables (Red and black) are comes next
ON THE Rv. Find a compartment as close to the batteries as possible but NOT in teh same air space. You do not want the inverter to "Breath" battery fumes.
Find a place to mount the inverter
Now measure for cable length.
Connecting.
Connect Black (negative) and Red (Positive) to the Inverter, Tighten nuts well, Tape the red and black wires side by side together (like lamp cord) till you get to the end of the red, Attach the fuse holder and the short red cable, Connect First red, then Black to battery (Again red to positive)
Turn on inverter and test
Run an extension cord (I like 12ga cords but for a short run and a small 'Fridge 14 shoudl do) to the Fridge.
NOTE: your batteries WILL run down in transit. The tow vehi8cle will NOT charge fast enough.
Note two: 1000 watt iverters the recommended MINIMUM battery is a 4D or a pair of GC-2 Golf car batteries.. Add a 2nd one (or pair) for each thousand watts.
Half the recommended will work, but will run down faster.