So, Sean O'Neil wrote:
"....What are the odds that the shore power is
charging the battery during plugin time? If it doesn't work that way is
there any way I can get it to?..."

Sean, I'd like to do this very same thing, and have been thinking
about the best way to accomplish it.  I think that David Schwarze's
idea of taking the outside  case off a battery charger and mounting
it permanently inside the camper is good.  Ideally, one could plug
in and simultaneously get AC to the camper, plus have the current
go to the charger to the barttery (or second battery).  Or, if
you're like me, you'd like to have enough batteries for about
600 amp hours camping fun (not counting your ignition battery  ;)

/martha