2003 Jeep Grand Cherokee clunking and resistance moving when in four wheel drive?

People like you - who have no clue how a 4x4 operates - should not own one.

First - you should only switch into 4x4 when on dirt roads, snow, ice, or wet raining roads.
Second - all four tires should be identical - same make, same model, and same number of miles.

When you engage 4x4 two things happen. First, power is taken from the transmission and transferred to the 'transfer case'. That power is sent to the front driveshaft with distributes it to the left and right front wheels from the front differential. Each front tire will have a locking hub - some are automatic and manual back up, some are just manual.

That stuttering and difficulty/resistance when making turns? That is your front hubs being very, very unhappy because you are on solid pavement and/or you front tires are not matching. You are literally tearing up your 4x4 front end.

When you exit 4x4 your vehicle should near instantly disengage those front hubs. Running it with those engaged is going to cost you thousands of fix, and since this is a 2003 - it will cost you the vehicle.

When you exit 4x4 you need to make those hubs disengage. If they wont come out on their own - then stop the vehicle and manually unlock the front hubs. You will find a movable sleeve at the center of your front tires, turn it. Sometimes you just need come out of 4x4 and just put the thing in reverse and you will hear the hubs drop out. Others you need to put the vehicle in neutral, then come out of 4x4 for the hubs to drop out.

The reason having identical tires are important - in 4x4 all the tires are locked together by gears - if three tires are Brand A and one tire is Brand X the Brand X is going to be a tiny big bigger or smaller. Bigger - it will bind up it's gear - all of the tires loose torque (power) - and the bound gear is prone to failure. Smaller, the other three will be forced to bind, torque will be lost (lost power) and all the gears along the drive train will get excessive wear and tear.

That you think this is transfer case fluid related - is scary. That like someone giving your chicken noodle soup for a broken leg.

The front end doesn't have a differential when put in 4WD . All my 4WD vehicles do this when put in 4WD . Try putting your Jeep back in 2WD then backup a few feet before going on . This may help the front end to release quicker .

4WD should only be engaged on a surface that allows slippage (ice, snow, dirt) or the front wheels will "hop". Any clunking can be bad u-joints or other front end parts. If you don't understand the mechanics of it, RTFM and/or take it to a mechanic.

The Selec-Trac 4 Full Time mode allows the wheels to turn at different speeds, which eliminates driveline binding and component wear that is normally associated with driving the vehicle in the 4 PART TIME position on dry hard
surfaced roads. My guess is that you used 4 PART TIME too much when you shouldn't have and damaged the transfer case. A new one will set you back about $800.

Your front CV joint is most likely shot, have it checked out: if it comes apart you will loose the whole wheel on that side and to a lot of damage to your vehicle and if you have an accident you will be ticketed for driving an unsafe vehicle. That is points and HIGHER INSURANCE cost.

Those cars are as badass as Dwayne The Rock Johnson. Keep it no matter what

No, DUMMY. The noise you hear are the universal joints in the driveline catching and binding because you're using 4-wheel drive on clear, dry pavement. If you continue to do this, you COULD damage your driveline.
You should ONLY use the 4x4 when driving in snow or on loose surfaces like dirt or sand. When you switch from 4x4 back to 2wd, back the car in reverse for about 20 feet before driving forward again.

See a Jeep or 4x4 specialist. Something wrong with the transmission.