If your AWD includes insurance, you won't be able to remove the insurance (and if you did, it would notlower the rate).

The included insurance is likely to be better than the amex insurance anyway, as if you insure through Avis (for LDW) and there is damage to the car, you have no hassle except filling out a form. if you dependon Amex, you need to pay avis for the damageand then file a claim with amex (who will likely want your primary insurance to cover it if possible before they pay).