I'm going to suggest you take both pistols, one on your person/in reach for the entire trip and the other locked & hidden in the trunk, maybe under the floor in the spare tire area or similar. Why you ask, well if you did run into trouble and had to use your pistol to defend yourself the LEO where it happened would place your pistol in evidence and it will be a while before you see it again. I personally wouldn't want to suddenly be 1000+ miles from home with no means of self defense to get back. When I travel by air I always have a minimum of 2 handguns, usually 3 pistols and a broken down AR, I've got a case specifically for this. When I travel by vehicle I usually have at least that but most likely more.
Kind of after the fact since this trip was over 2 months ago...