in your situation, SUV sounds a good choice.

For most cases, 4WD is adequate.  You don't have to have AWD.  AWD is less fuel efficient.  You know the difference between 4WD and AWD, right?

In terms of breaking problem with your Corolla, that might not be due to the problem in sedan per se. It is more likely due to worn out tires, uneven breaking, or wheel misalignment.  In normal condition, Corolla should have the same breaking performance as SUV. If that happened on very slippy surface, almost any car or SUV will spin around.