I like the 2 deep cycle batteries idea. Easier to set up and none of the complications of switching. They would be wired in parallel I assume?
For two 12s, yes parallel.
The main drawback to the two paralleled into a full-time bank(one big battery), is lifespan.
All lead-acid batteries have lifespans measured in charge/discharge cycles. Take it down like 20% and recharge and get maybe 3,000 cycles (depending on who made the battery). Take it down 50% and get maybe 1,000 cycles. Take it down 100% and get maybe 300 cycles. (That's for deep cycle type. Cranking type might be wasted after half a dozen deep drains.)
With two in parallel they'll both be going down and up together, and they'll both wear out around the same time. A dedicated starting battery only being drained 1/2% and then recharged will last a whole lot of cycles. The deep cycle, being drained more deeply won't last as long.
Another potential problem is chronic undercharging. Most people don't drive enough hours to fully recharge a battery that has been taken down a good ways (typically say 50%). Letting a lead-acid battery sit around less than fully charged also shortens life.
With a dedicated battery, the starting battery gets drained very little and recharges in a few minutes. The deep cycle might not get fully recharged, but that won't shorten the life of the starting battery.
But with a pair in a full-time bank, both batteries will experience the same usage, and whatever shortens the life of one shortens the life of both.
There's no right way or wrong way here - just different pros and cons.
Would there be any issue hooking up a 100w solar panel? There will be times when we are parked up for a couple of days and need to keep the cooler running. I'm thinking it's no more complicated than connecting the solar charge controller to the batteries?
Yea, no big deal. Permanently tied together it's just one big battery. Doesn't matter which you connect the charge controller to.