The fuse panel you are showing is the 12VDC FUSE PANEL.
Your Air COnditioner is operated from 120VAC and will have a CIRCUIT BREAKER in the Power Distribution panel controlling it. You will see the 120VAC Circuit breakers to the left of your photo shown here.
The only requirement for the 12VDC with the Air Conditioner is to power up the thermostat...

bsmith image
If you are plugged into a 15-AMP Receptacle in the house/garage using an extension cord and RV Adapter then your RV air condition can trip your house 15A breaker during heavy use. You may have other items in the house also using power from the same 120VAC circuit breaker zone.
My house was wired with 12gauge electrical wiring and I have a separate 20AMP Circuit breaker that was installed for a compressor unit in the garage. This is the only thing on the 20AMP Circuit. I use this for my RV connection using a RV LONG Adapter cord.
In you case I would find a 15A Circuit breaker zone that doesn't have any other appliances or lights on the same circuit if possible. The garage is always a good place to plug in and usually it only has a few lights and a couple of 120VAC receptacles scattered around the wall. Just keep the lights OFF and make sure nothing is plugged in to any of the garage recepacles...
Just my thoughts here...
Roy Ken