I just started towing an RPod 173 with a 2008 Rubicon.
my 173 weighs 2150lbs. My 173 is about 400 lb lighter than your 182.
there have been some improvement in the jeep rubicon since mine was made on 08.
My jeep has the 4 spd auto and you will have either 6 spd manual or 5 speed auto. you will also have the new Pentaflex engine with about 25 or so more HP and more torque. This all matters.
I pull mine in 3rd gear with overdrive off. I cruise at 55-60 at 2500 rpm. I am at my limits of capacity with that. I cant get torque converter lockup in overdrive so I keep it off and cruise in 3rd. I do pull it steady with no seesawing, no swaying, tracks like a dream, electric brakes work quite well. So far I am pleased and satisfied that I can tow anywhere I want. at 2500 rpm the engine is not over revving and not overheating and my tranny is cool and good.
you will be able to do better with your increase in power and torque and more gears. You will be towing in higher gear at lower rpms and can downshift when you need to higher rpms and more power without having to be in too low a gear.
you will find that every lb of weight matters. I plan on taking off my hard top and travelling with my trek top which will save about 150lbs. going to take one propane bottle, keep water tanks empty till I get to where Im going, carry minimal extra clothing and general gear.
keep to minimal weight on gear and stuff you plan to travel with.
may have to keep speeds aroung 60 or so but thats OK with me. Mileage will drop drmatically as mine is around 10-12
remember the rubicon is very hevay duty with oversize axles and differntials, heavier shoks, springs, overall suspension. bigger brakes etc. It all helps. THe Jeep is plenty strong and can handle the load on the frame and suspension. You may consider a tranny cooler add on too. I have flash chip that also gives me a bit more HP that could help you too.
I think you will be fine. I kow of a few other Jeepers pulling trailers in this weight class and are doing fine. and they arent in Rubicons.
I think you will be happy but it wont be like pulling a jet ski behind you.
If you think you are cutting it to close you may consider other 4X4s if you arent stuck on a jeep (I am so I accept the comprimises)
If you can find a good jeep Commander with a bigger engine that is a kick arse rig, a Grand Cherokee, of a Ford F-150 Pickup, severl other vehicles could fit your needs with more power.
see my post under camping in Ocala.
good luck