You are out of luck using a trunk mount / strap-on bike rack on the 1999 Isuzu Rodeo because, as you thought correctly, the spare tire will be in the way. Also, even if your 1999 Isuzu Rodeo did not have a spare tire mounted on the rear, the major car rack companies such as Thule Racks and Yakima Racks do not advise transporting more than 2 bicycles on a trunk rack attached to the 1999 Rodeo model.
The
SportRack A30813STL Spare Tire Bike Rack is a very cool option though. It mounts to your spare tire and will also let you carry 3 bikes. Most other spare tire mount bike racks are only rated to handle 2 bikes.