Olddawgsrule,
Ok you're right on the methane, we got way off topic.
At the risk of restarting an argument I'd really like to better understand the fear folks seem to have of charging their house batts from the TV. And what they expect a solar charge controller to do to improve things.
Do your house batts get charged that way while you're driving? If so, what's the difference? Most all class A, B, and C RV's charge that way too. Always have.
You need a solar charge controller for two reasons. First, nominal 12V solar modules have an open circuit voltage of 18-20 volts or more. That's just the way PV devices work in order that their max power point voltage is in a good range for battery charging (around 13-14V). As the battery voltage rises their current output reduces until it reaches zero at that 18-20-ish open circuit point.
Second, people leave their solar modules connected to their batteries more or less permanently. So, when you leave a solar module connected to a battery for a long period with no load or charge controlller on it the battery voltage will keep increasing until the current output by the solar module drops to a level that matches what the battery can accept just floating. That is typically a very high voltage and results in excessive generation of hydrogen and oxygen consuming the water in the battery. Not good.
In contrast, your TV will never be left running and connected to your house batteries for long periods. And, car alternators are self-regulated to 14.4V. So neither condition requiring the use of charge controllers in solar applications applies.
Also, the chemistry used in your TV start battery is essentially the same as in a flooded lead acid golf cart battery. So if getting charged from your TV alternator was going to be a problem for the trailer house batteries then it would also be one for your TV start battery. That doesn't happen. This all supposes that you are not using some exotic battery chemistry in your trailer of course.
So, the problem with charging from your TV isn't that you risk battery damage, its that your TV alt has trouble putting out enough current at high enough voltage to be an efficient charge source when being spun by a big engine. You can partially get past the need for higher voltage by running big conductors, but we're talking about a lot of copper.
If you turn the TV around nose to nose with the trailer you can get to maybe a minimum 10 ft conductor run. 1/0 would give you a voltage drop of 0.2A at 100A, if your alt could put that much out at idle. And to that you need to add connector losses at both batteries and at whatever mating connector you use between the batteries. The connector losses from using jumper cables are too high because of the limited connection surface area, terminal lugs should be used like on any other battery connection.
Then there is the inrush current when you initially hook up the two batteries at different voltages (the additional current will come from the TV battery, not the alt).
BTW, all these same considerations will apply to a solar charge controller in the same circuit. How do you keep from finding out where they hid the smoke in your solar charge controller from the excess current when you first connect up? Batteries are essentially an infinite current source while solar modules are current limited. That's what I'd be worried about.
Welding cable is good for this application because its flexible, try to bend normal 1/0 sometime and you'll see what I mean. Ampacity (ability to handle current without overheating for 1/0 welding cable is about 200A, which I think would be safe considering the inrush current when you initially connect up the two batteries. So I think 1/0 would be the way to go. I would use mating high current Anderson connectors so you can't accidentally mix up the battery polarities. They're rated for hot connection too. Conceal the set on the TV behind the front bumper or somewhere else accessible. Have the mating connector and its cable looped and strapped to the the trailer tongue. Anderson also makes nice rubber boots for these to keep the road crud out of them.
If your TV alt doesn't put out enough current to make this worthwhile the car audio industry has a solution that the folks installing giant amps in their vehicles use. There are several companies that will wind you a custom alternator. Just be sure to tell them that you want to maximize output at idle, not at normal engine rpm. You can also try a smaller diameter sheave/pulley on your existing alt.
So charging directly from the TV is a perfectly viable solution, I'd do it with no qualms at all, but it doesn't address my need for an AC source for the air conditioner and microwave. So I still lug my generator around, for now. But if you already have a large inverter or don't need to run your AC appliances, then TV charging is a great way to go.