It really depends on how you use your trailer. Furnace blower is the largest draw. With furnace expect 1 nigh of use per battery. In a mild climate figure 2 nights per battery.
After that wanton use of lights will be a big draw unless you have LED bulbs.
It's easy for us to spend your money. I'll bet that four 6 volt batteries and 300 watts of solar will put you back $1000 without even knowing if you even need to spend it. My opinion is I would use two 6 volt batteries from Sams Club or Costco wired in series. Charge the batteries full, get a set of jumper cables and go camping. If your batteries get low hook the jumper cables from the vehicle to the trailer and let it idle for 2 - 3 hours. If you make it three days then add solar and you'll probably make it a week without having to haul another 100 lbs of tongue for extra batteries.