Good advice above!
The battery amp hour size gets you from one charge cycle to the next. However, if you do not have enough charging, it does not matter how big the battery is. It will be drained sooner or later.
85 amp hours is enough for one night, maybe two, of lights and frig controls, etc. 110 amp hours will get you two or three nights. 200 amp hours will get you 5 to 7 days. Running a propane furnace that has a big fan will cut that almost in half in cold weather.
In all cases, you need to replace substantial charge before the next dry camping event. Periodically you need to do a 14 to 18 hour full clean charge to keep the lead acid battery healthy. Maybe once per week.
Assuming the engine does not charge the TT battery, and you do not run the furnace, you could stay at a camp ground using shore power every other night. With a bigger battery you could delay the campground hook up another night or two.
A robust charge from driving 6 or more hours a day would keep even an 85 amp hour charged enough for dry camping every night. Running the furnace may or may not work out after a couple of nights. Test it to find out.
I recommend you get a cheap digital multi-meter from your local hardware store. Use it to monitor voltage at the battery terminals until you know how the charging and discharging is performing.
You can measure tow vehicle charging of your TT batteries by measuring current and voltage while the engine is running. Some tow vehicles need to be running faster than an idle to charge. Do this at the connector between TT and TV. Measuring current is not the easiest thing to set up, but it would be the best way. You will need a 40 amp current meter for this.
Measure voltage on TT batteries first and then start the engine. It should be below 12.4 volts for this test to start with. Discharge to 12.4 volts or less first if necessary. You should see 10 to 30 amps flowing. Voltage should slowly rise in an hour or so. 30 amps would be an excellent charge rate for an 85 amp hour battery. Less than 10 would be a problem.
I assume you have a 7 pin tow connector. Increase the size of both ground and positive 12 volt pin and engine alternator to increase current flow. Check for loose or corroded connectors. There will be a fuse or circuit breaker in the positive side of the circuit. I used 8 gauge multi-strand wire for mine.
If you canít or wonít measure the current, you can easily measure terminal voltage. There are three basic voltage profiles for lead acid batteries. They are: Charging, Discharging, and Static. Charging profile tells you how the charging device (your engine alternator) is performing. Static profile will tell you what the current state of charge is in the battery. Use a chart to convert voltage to percent of charge or use the percent charge meter in your TT. Static means not charging or discharging for 4 hours or more.
Discharging profile will always have a voltage lower the Static.
Note, checking the voltage in the tow vehicle works for the engine start battery. It is often not accurate for the TT house battery. Check at the house battery terminals for more accurate results.
Start at home. Measure the battery terminal voltage. Start with the battery terminal voltage below 12.4 volts. Hook up the tow vehicle and start the engine. The voltage should slowly rise to more than 13.3 volts. It may take 4 hours or more. Final charging phase should be 13.6 volts or more. At this point the battery is not fully charged. It takes 14 to 18 hours to do a full clean charge. Voltage will stay the same for the remainder of the charge. This is the charging profile.
If the voltage does not rise at all, then the engine alternator is not charging the battery. If the voltage is not above 13.3 after four hours, the charge is below optimum. Increase the size of both ground to 7 pin and positive 12 volt pin to engine alternator to increase current flow. Check for loose or corroded connectors.
I wish you good luck and happy trails ahead!