You need to get your battery system up to par before you start looking into solar. The solar is not going to power your items directly, it is going to charge the battery.
Step one would be a large 12V group 31 battery. Better yet is a pair of 6V golf cart batteries. We can make a 3 day weekend easily with our pair of 6V batteries, but for just the fridge, water pump, and moderate lights a single 12V will work for us as well.
Step two would be converting your lighting to LED bulbs. Available on ebay from China suppliers for less than $3/bulb. LED's use a small fraction of energy compared to incandescent bulbs that you currently have.
Step three would then be adding a solar system after the first two are complete if you still are wanting more. For weekend trips its probably easier and more cost effective to add additional battery capacity. I think solar comes into play when you are out for a week at a time and it is not feasible to carry a battery bank that will last that long.
As for charging with a generator, you want to plug the generator into the trailers shore power cord. Then the onboard converter/charger will charge the battery.