First thing, please get more strips today. Whether it's AT strips from the vet or getting a human meter as a backup. It's always good to have a back up meter. I haven't seen any spreadsheet updates for a few days.
Next, onto your questions. I travelled by car from Vancouver to Fort Collins with Neko, there and back, a trip of three full days of driving each way. It was during the summer and hot. I had a cooler with gel packs in it. The Lantus was wrapped in bubble wrap inside a small Tupperware. The bubble wrap and Tupperware made sure it didn't move around and kept some separation from the gel packs. I refroze the gel packs in the hotel room freezer. The one hotel that didn't have a freezer in the room let me keep it in their big kitchen freezer to refreeze overnight. I did check that all the hotels we were going to had a fridge. I also used the cooler to keep some water cool and for opened cans of cat food. Make sure you take low carb and high carb food, maybe honey or karo and plenty of test strips. Some cats (mine) went diving during the car ride. Not all will eat during the ride either, though mine did.
My insulin was fine for the above trip. On a second trip (flight), I got a Frio wallet. People use them for keeping insulin cool for a while. I still had the Frio wallet inside a small lunch size cooler with small gel pack. If you don't keep your insulin cool for what looks like 36 hours or so, you may shorten it's life span.