Extra charging power

Just add the batteries but use an isolator. That is simply a block with diodes inside. Diodes are one-way valves for electrical current flow. When the engine is running, current will flow out of the block two ways. One is to charge the truck's batteries and the other is to charge the add-on batteries. The unit isolates the add-on batteries from the truck's entire electrical system when the engine is off. That means you can totally discharge your camping batteries, but the engine will still crank normally.

You may need to visit an RV shop for this. Almost all RVs use one of these.

Using a larger generator isn't going to help, especially if you are driving many hours at a time. Your generator is large enough already to charge the truck batteries and run the entire electrical system. A larger generator, in theory, would only allow that to happen faster, but batteries can only accept a limited charge rate before they become overheated and plates start to warp and short. Your truck batteries have to be recharged enough very quickly to handle another cranking attempt, as in when you do a lot of short-trip driving. After the first few minutes, the charge current will drop down quite a bit. To say that a different way, after the first few minutes, the generator is running at a faction of its maximum capacity. There is plenty of unused current capacity to charge the camping batteries.

You can run into another problem by installing a higher-current generator. Most vehicles can be found to have one of multiple generator sizes, electrically-speaking, and the fuse in the fuse box, or the fuse link wire, is sized accordingly when they build the wiring harness. A generator with a larger maximum current capacity could develop enough current to burn out the fuse device. This is most likely to occur when the charging system is being professionally-tested for maximum full-load output current. The test is only done for a few seconds to prevent overheating the generator, but that is enough to pop a fuse.