You have a lot of good advice already but also some not so correct advice.
Like others have said your PD 4000 Power Control Center charging system in the TCer only works when plugged in. You can use this when traveling but in my opinion it is more hassle than it is worth. What others have done, and this is done more often in a motor home, van or Unimog type build is to have an inverter convert 12v power to 110v ac and run your power cord to your charging system. This will then run your charging system as you drive - good points is that it will work as intended - bad points is that in my opinion you are killing a mosquito with a bazooka especially in a tcer.
Running your truck to charge your batteries is again going to do the job BUT you are running a HUGE engine for a trickle charge at the best. Calculating the distance from the truck to the camper batteries the wire gauge that you will need to make this efficient and doable is overkill not to mention the fuel use to get a little charge from the engine. Large cables are a good idea in any case but not for what you want to do, just not going to get the amps you need in a reasonable time.
There are a lot of other systems/ ideas but really you are overthinking this without looking at the simple fixes first. First figure out what you need for power. It may make more sense adding a different heating source like a vented cat furnace that takes less draw on the batteries. OR pick up a cheap generator and run that to charge using your power center, you may have to update/ enlarge the power center to charge faster so you can cut down on generator run time. If you are in an area that you are not going to tick off neighbors by running your truck half the night then you do not need the quietest generator. If you are close to being good with two batteries maybe switching to 4 6V or another 12V would do it. Solar may work BUT when you say you are running your furnace I figure that it is winter and your solar does not give you the most power during the winter so your actual charge this way may not be enough. Add more insulation to the camper, this will take less power to heat it and your savings are not only in the 12V you save but in the propane and the noise of the furnace running. If your batteries are exposed to the cold try moving them where it is a little warmer, this will help to give you some extra power.
With my tcer I had two group 31 deep cycles and I could camp in -30C with a lot of power left over the next day. A couple hours driving would top them up pretty good - not full but enough that I could get another night out of them and still had a little remaining - usually by the third day I knew I was pushing another night if it did not warm up. If I was out for a long time in the real cold I would find a plugin during the day or a night every three nights and top up. Or I would take the generator and run that for a couple hours when making supper each night so I would not have to do a HUGE charge when I was desperate.
Side note:
Currently I have a small class C that has 4 6v and is well insulated. So far most winter nights I have had power to plug into (old = wimp) but I did notice the few nights I did not have power that the batteries were not that low the next day, insulation does sure help. It also helps as I have HUGE wires running from a heavy duty alternator to the camper batteries to charge when driving but I would still not run the RV motor to get that charge. My current Class B conversion has two 12 starter batteries and 1 12 deep cycle Group 31 running a Espar heater and used it the other night and the deep cycle battery was 95% full in the morning - was only -6C during the night but was happy with that. Started the van and in 30 minutes of driving the group 31 was full. Again the benefit of the larger cables, lower electrical needs so less time needed to get back to full charge.
