Before I saw the date, I was thinking "who the heck uses the dealer this late in the game?"

bilzhome, I would like to say it's a corroded/shorted wiring issue on a 96.. you may want to post in the 1st Gen Dakota forum though, they can probably be a better help.
https://dodgeforum.com/forum/1st-gen-dakota-66/

 

old thread but I would suggest getting a higher rated alternator from the 4.7 durango? but it sounds like there must be some kind of parasitic current draw and not a charging system issue

 

I would avoid the stealership, and go with a shop that specializes in automotive electrical. Unlike dealerships, success in repairs determines whether or not their doors stay open. And all they do is chase down electrical issues, so they are pretty good at it.