shutting down the Refrig or keep it On between trips

An absorption fridge running on AC power uses somewhere around 4 to 6 kWh per day, considerably more than a compressor fridge (which these days may average around 1 kWh per day or so). You know your electric rates better than I do, of course, and so can better figure the actual cost.

I personally would turn it off rather than spending maybe $10 for each two-week period; the money (and general energy) savings would outweigh the annoyance.