Go to Lazy Days and hook up to another similar camper. Check the lights. Take that camper, hook to shore power. Then rehook to this camper and check the lights. If the module blows then it's your Jeep. If it all works well with a different camper, then it's your camper. With this test Lazy Days and you will know exactly where the problem is.
Also, you could hook your trailer up to another vehicle, Chevy or Ford, or Dodge, etc. after it has been hooked to shore power and see if it affects a different vehicle. If it blows with another vehicle, it's the camper. If it works with another vehicle, it's your Jeep.