Seems to me that your inside battery monitor is telling you that you have a bad connection somewhere. You probably remember the days when you got your first car and had to clean the battery terminals, add water, check the cables, tighten the ground connection. Same thing needs to be done here. Do all that first, then do your voltage measurements at the batteries while on shore power, off shore power, with engine running, without engine running. Save all those measurements in your historical data spreadsheet.
The voltages shown on the panel inside the RV are just a guide, don't use them as actual voltages.
As far as battery types, if you need new batts, the 6V golf cart batts are the best for an RV'er. A search of Google will turn up the reasoning. Costco has them for $80 each.
You can limp along with weak batteries for months if need be. But you shouldn't.