Based on what I am seeing in the posts, this is my take on it:
0) Batteries, generators, charging systems, and camper electrical systems are expensive items. I recommend following the guidelines in the owners manuals. I would be very careful what gets hooked into the camper's 12V
electrical system since that has the potential of taking out any appliance or system connected to it.
If you want to play, make sure the battery is disconnected from the camper electrical system first. If you are going to connect a standard issue battery charger to the battery, I would do the same, disconnect the battery from the camper!!
1) The fancy charger in the camper is probably the best way to charge a battery, assuming it is working correctly and isn't an old Univolt. It is designed to charge the battery quickly and keep it charged without overcharging it and damaging the battery.
2) Using a standard battery charger running off an inverter style generator and then putting the generator's 12V
power in parallel with it might not cause any problems. I am concerned that the designers of the generator didn't think that possibility through, although it is possible they did and tested for it.
My concern is that the parallel setup of the charger and the generator has the potential of blowing out the transistors and diodes in the generator that are used to generate the 12V
. Depending on how it would fail, it might take out the entire inverter.
Also be aware that what works fine with last years generator may not work with this years because something got changed or "cost reduced" during the manufacturing process.
3) As we all know, camper batteries aren't inexpensive. Beating them to death is only going to shorten their life. Over discharging or charging them really does them in. I have seen brand new batteries destroyed over a weekend, expensive Optima Deep Cycle Gel Cells, by someone being careless. If you have a generator, keep the batteries charged to a reasonable level. Keeping the batteries at a decent charge level should take less fuel than trying to bring them back from the dead, they will last longer to boot.
As far as using the generator to charge the battery, the generator probably puts out 13.8 V plus or minus some amount, which won't overcharge a battery assuming it isn't left connected indefinitely.
4) There are applications and systems that are designed to deal with multiple chargers. These are either older designs that aren't particularly sophisticated (like a basic diesel generator set) or they are modern and are specifically designed to deal with it. Just because it works in one application, doesn't mean it will work with your camper.
Running the camper charger off of the generator is my vote. If the vehicle battery needs a little help, hook up the umbilical and let the camper charger do that to (unless you have one of those battery isolators which won't connect the vehicle battery / charging system to the camper without the engine running). Try to keep a reasonable charge on the batteries, trying to eek out the last bit of juice in a battery shortens its life.