The Alternator's effectiveness is directly realted to how long one drives, the thickness and length of the copper between alternator and house battery, and most importantly, the vehicle's voltage regulator, over which one usually has Zero control.
My battery yesterday at 14.7v was taking 29 alternator amps. When I reduced voltage to 13.7v, it took only 9 amps from the alternator.
HUGE difference, and most vehicles do not allow 14.7v for very long as they never were designed to recharge a depleted battery tacked onto the alternator charging circuit, but they were designed to prevent serious overcharging, thus the premature drop to 13.7v. What voltage is chosen and how it is chosen varies very widely among different vehicle platforms.
So By all means utilize the alternator, it is foolish not to, but do not expect it to have the time or be allowed to attain the voltage which can then charge the battery at the limit of its acceptance, and also Know that 80 to 100% charged takes 3 to 4 hours NO Matter what, and without ever reaching a true 100% charged, the battery is doomed to early failure.
Early morning alternator to bring battery to 80% is good, when followed by enough Solar wattage to finish off the task, or nearly so.
Also have a plug in charging source for if/When one does have access to grid power. Aim for no less than 20 amps per 100Ah of capacity.
You can beat the F out of a battery, and still get An Ok life from it, IF you can occassionally fully charge it, however long that takes, and an abused battery can take a long long time to get there, usually requiring the automatic plug in charging source be tricked multiple times into restarting.
Restarting it requires one load battery with high loads until battery voltage drops below 12.6v, then restarting charger, then removing loads.
A hydrometer on a flooded battery will show that multiple restarts of the 'smart' charger are usually required.
All 3 of these charging sources can be tweaked/chosen/ modified to perform better, but this can overwhelm the Newb trying to get an overall grasp of it.
For solar, Aim for as much as your roof will allow and get a solar controller which allows some adjustability as to absorption voltage and duration, if possible.
For the alternator charge path, use thick copper from to alternator (+) output stud to isolation device, to Fuse, to Aux battery. Ground it back to the alternator mounting bolt or (-) output stud, with equally thick copper. Not much can be done for the vehicle's voltage regulator's Unideal allowed voltages, not for a Newb not willing to spend 2 to 4 C notes for a DC to DC converter, and the time to true full charge is still 3 to 4 hours from 80% charged.
For the plug in charger, One which can power all DC loads while charging the battery, without gettng confused by the cycling of the compressor fridge, can go a long way in getting acceptable lifespan from a battery. "Garage" chargers vary widely in how well they do. RV converters generally do better, but do not come with sey casings, alligator clips, or blinking lights that also promise to preform oral sex on you like the garage charger marketers claim.
When the battery fails, replace it. It is only rented anyway. the length of the contract is the variable depending on its treatment. It kind of sucks when its capacity is so comnpromised the fridge appears to not be working properly anymore, but just know when the fridge becomes unreliable you should be considering a location where it is not so hard to replace the battery.
Many people can get away with very substandard charging methods, as long as they accept the battery will not live long, and not be very reliable. At some point this person perhaps gets tired of trying to warranty or purchase batteries, then steps up the charging equipment.
It does not all have to be done at once.
I would recommend the compressor fridge get a dedicated 10 AWG circuit, and not rely on existing vehicle Ciggy plug 12v receptacles. Better yet is to bypass the Ciggy plug and receptacle and wire it right to Fuse block. Make sure the vents on the fridge are not restricted whereever it is located, and that it does not bake in a hot vehicle .
Streaming videos likely will use 3 to 4x as much electricity as the fridge uses in that same time span.