Will the DC charger for the 2nd battery affect any peripherals while charging?
In short: no, there should be no problem.
There's no reverse polarity, so nothing to worry about there.
Yes, the voltage gets higher when the battery is charging, but that's exactly what happens in a car anyway when the alternator is charging the battery. Electronics built for a car's &quot;12V&quot; already have those voltage variations in mind. Usually they will operate correctly in a range of something like 10 to 16 volts, and tolerate brief spikes of 20V without damage.
These are just rough numbers, and you should look at datasheets or manuals (if available) for anything you want to plug in, but my point is that it looks like what you're creating is no worse than a normal car environment, so anything that works fine in a car normally should keep working fine.