The Model 32 part number 903211000 you mentioned references a Kwikee 32 series powered double step just like the part # LC3722616 that you referenced so this is what you'd need. view full answer...
You could attach the mounting bracket to the rear bumper of your 2010 Jeep Wrangler of the Brophy Steps part # SS03 so that you could use the steps of the kit for your dog to get in and out easily. view full answer...