Feel free to include your rig and location in the iRV2 profile section. You can also post you TT and tow vehicle in your Signature. It helps us answer your questions.
Dry camping for a night in a 32 foot 5th wheel TT should be easy. I guess you have more than 200 amp hours in your battery bank. You should be easily able to run 12 volt lights, controls for propane water heater, propane refrigerator, and TV or computers. Running the inverter for 3 or 4 hours should also be good.
Recharging while driving will replenish some of the used power. Get a full recharge over 14 hours at your next shore power site.
I get by for 5 days in the summer without the furnace and 3 days in cold weather with the furnace. I only run the inverter for short periods for small appliances like laptop charging. My rig is smaller than yours and has a 30 amp service. Your systems may consume a little more 12 volt power than mine. Your furnace may use more than my small furnace.
Test your system to see what you get. At your next full hook up site, delay connecting the electric and try running off the batteries.
A small generator will provide battery charging. You must run it for a significant time to charge lead acid batteries. 4 hours may get a 50% to 80% charge.
You can plug your 50 amp system into a small generator using adapters. Your on board charger will do the charging. Get a full 100% charge at your next shore power site. A 50 amp to 30 adapter plus a 30 to 15 amp combination would be clumsy but doable.
My small 30 amp on board charger works fine on a 1000 watt Honda generator 400 watts.
50 amp - 700 watts
75 amp - 1200 watts
Many people choose a 2000 watt generator. They are light enough to lift into a pickup bed. They are powerful enough to charge batteries and usually a microwave at the same time. Some people manipulate their loads enough to run an air conditioner.
There are a few portable generators with 30 amp 120 volt outlets. Honda makes a 2000 watt gen with one. You would still need a 50 to 30 adapter to plug in the 50 amp cord. Cheaper 2000 watt generators are widely available and would work fine for occasional use. Check older iRV2 posts for recommendations.
A 3500 watt generator would weight more. It would run your AC appliances with careful energy management.
Construction open type generators are much too noisy for most camping situations. Be sure to pick a quiet inverter generator.
I wish you good luck and happy trails ahead!