candied mints storage and transporting long distance
Your main limiting factor is the butter, which can go rancid and it highly sensitive to warm temperatures.

You should freeze the mints for storage until you take your trip.  You don't want them absorbing moisture or off flavors, so you want to wrap them very well, using freezer grade storage bags.  I would suggest double bagging, small bags in larger ones.

Get a cooler large enough to take the mints on the car trip, packing it with dry ice (which you can buy) or commercial freezer packs (sometimes called blue ice, such as this product on Amazon) to keep the butter at least cool for the duration of the car trip.  

You may need to plan to find a purveyor of dry ice at one of the places you stop during the trip, or arrange to have your freezer packs rechilled along the way.