I have always only put Chloe in her kennel but my husband uses a car harness.
I think I am going to switch to the car harness too. At our last puppy school class, the instructor was asked about what to do about a dog whining all the way to class even though it was on someone's lap. The first thing the instructor said was "WHY is the puppy on a lap?" They are a projectile in an accident (or even a sudden stop) which is not safe for anyone. And I thought I was being safe by keeping her in the kennel but unless the kennel is strapped down somehow and/or somewhere where it won't move, the kennel is also a projectile. For some reason, I never thought of that.