You have a huge problem with insulation, even in full sun, if a 5000btu does not work. First priority is the rip it apart and insulate it. minimum 2 inches on the roof/ceiling and 1 on the wall. I would go 3 roof and 2 walls if you can spare the space. Be careful that your steel frame is not going to radiate heat/cold across the walls too, keep them insulated from the inside, thus 2 inches on the wall - 1 inch between the frames and another inch inside that will isolate the frame from the inside walls. Same for roof - to isolate the metal from the inside. On mine I used 1 inch wood for the inside inch frame work, and the outside is the trailer's steel frame. Aluminum frame is worse in this case as it transfers heat faster.
My trailer is a similar size and after it gets cool, 20 mins max, the compressor on AC unit cycles 1 minute out of 10. I have a 9200 btu, so about twice yours, but 1 min out of 10 if not a factor of two keep in mind, factor of 10.
9200btu or below will run on the 2200 inverter generators, but not a 1000. If yours runs on a 1000 then great.
I advise using the generator as the batteries will take up a lot of space, be really heavy and require a lot of charging (forget parking in the shade if u want the solar to charge them) and will be very heavy, needlessly heavy. Do not put this much weight on the tongue, place is over the wheels/axles as tongue weight is a huge deal and overloadeing tongue will overload your trucks rear and cause driving issues and be a safety hazard. Consider where you will travel to. Out west the nights are always cold, in the mountains the days are usually cool and dry... Make sure the AC is even going to be used a lot first.
A good generator should not give off gas odors. Since you have a trailer then keep the generator on the vehicle, farther away, preferable on a front hitch rack, and run your extension cord. 5000btu ac will not require a particularly heavy extension cord. My 9200 runs fine on a generic regular cord when I plug into the house, but the one in the truck is big. They make "extender" gas tanks that double your little generator's fuel capacity too. Mine runs 10 hours feeding the AC all night on 0.9 gallons.
With the generator this far away I cannot even hear it running, nor feel it. I have the power cord running inside the truck's frame to the back, hidden, safe and stealthy.
Black metal trailer frame going side to side with 1 inch pink foam, err it says 3/4 inch, so that must be the size of the frame.. Wood 1 inch strips made by cutting up a long 2x12 going long ways. More insulation went between the wood and the wood was easy to screw the ceiling panels to. Keep them exactly evenly spaced and mark where the wood is so you know where it is when you hide it with the ceiling panels.
With solar panels over the roof the ceiling does not get warm even.
I know you ordered a trailer with nice interior walls, but yea, you made a mistake. Suck it up princess. You might just have to swallow the fact that your walls get trashed so you can insulate it. Did you say aluminum walls? Lol, well, there is your problem with heat, and is why your walls are 88 degrees. This is one big radiator. Do not ever, under any circumstances use metal walls inside. This takes the heat from your aluminum exterior, aka, heat harvester, and radiates it through the metal frame to your inside metal walls, aka, heat sink.
So, rip out, shred, bend, break, whatever and remove the interior walls. Replace them with 1/8 inch wood panels or similar (fiberglass or whatever fancies your boat float but just not metal or anything that conducts heat this good). You will be very glad you did proper and correct insulation. This will pay off in spades. If you do not then my only advice is to sell the trailer and start over from scratch knowing what you know now and have it done right.