AI'm making my first journey with a cake, about 1.5 hours in Louisiana summer heat. It is going to be a two tier minnie mouse cake. I am planning to stack the cake on site. Does anyone have a recommendation on how to keep the icing from getting so warm is "squishes" out between layers? Maybe I need a stiff buttercream? I've had this problem recently with the icing melting right off a cake in this heat and humidity.

Precool you car - run the air for at least 10 minutes before putting the cake in.  Keep the air conditioning running full bore the whole time.

Make sure the cake is chilled before you put it in your car.

You can make a cooling chamber - put a block of ice wrapped in plastic in a box, then place the cake tier on top of that.   OR maybe wet some towels and freeze them; wrap them in plastic and wrap that around the cake box.

AI would use a buttercream that uses shorten Instead of butter also. Then make sure to use a thick stiff dam of buttercream inside to help the layers from squishing out. That's all I have sorry