Quick update.

The weather changed for one day. High of 11C this morning. -4C tonight again.

I was able to get under the Santa Fe and disconnect the viscous coupler. Pretty easy.

Car seems to work great as a FWD unit.

Druss100 was correct. My coupling is a HMC/KIA unit with a part number of 47800-39420

When Spring gets here, I will get after repairing the coupling.

 

My dealer was not of much help, so I took the Santa Fe to our local Mr. Transmission. In about 30 minutes they diagnosed the faulty coupler. They figured it was pretty much seized giving us the the driveline thump issue even with the unit disconnected. Diagnosis is free of charge.

Mr. Transmission could get me a coupler in 2-3 weeks, from Hyundai, for $1586.00. Installation in 1.3 hours.

They were good to chat with. I told them that I didn't want to keep the Santa Fe much longer. Costing me way too much in repairs. We talked about getting a used unit from a wrecker. I tried that. Seems like the rest of Ontario is trying that too. None to be found. But a gentleman at Andy's Auto Wreckers in London, Ontario had rebuilt and new units for sale. Rebuilt are $650.with 6 months warranty. New are $900.with one year warranty.. Mr. Transmission suggested the rebuilt unit, so I ordered one that arrived at my house in 3 days. Mr. Transmission installed it.

3 weeks now and all is good. The unit being possibly somewhat seized must have been putting some friction pressure on the drivetrain, because we can certainly tell that the overall driving experience is way smoother now.

Thanks all for helping me out.

Take care. Be safe. Now our problem is we have Covid. It's not nice.

 

My 2015 Santa Fe GLS had the exact same problem. The first time it happened I was pulling away from a stop sign. It "thumped" so hard I thought I'd been rear-ended!. Two different dealers were of no help. I found in an Aussie forum (I'm USA) that this happens more frequently when running AWD all the time but traveling on and off slippery surfaces. In other words, YOU have to turn it off and on when road conditions change. Possibly a poor design?
Anyway, you came up with the correct fix. A local, private shop finally diagnosed mine. Oddly enough, they only changed the diff and not the clutch pack, and of course the problem persisted but not as bad. I asked them to go back in and change the clutch pack as well.
In the end, it turns out that the diff and clutch pack BOTH need to be replaced. And yes, it's quite costly!!
A possibly related but maybe not problem: when pulling my small pontoon boat I smelled something hot and isolated it to the rear diff. It was quite hot! Since I was driving on a flat, dry road at ~50mph without the AWD on, this makes no sense. When I turned the traction control OFF, it immediately cooled down. While this makes no sense, I now turn traction control off when I pull the boat and have no problems. If I forget to turn off Traction Control, the rear diff gets hot. WEIRD! Any thoughts?