How do check transmission fluid level in a 99 durango correctly ?

I put a link below which give a number of things which could effect shifting.
If check engine light is on have the code read. It may help pin point the problem. Most auto part store where I live will check and give you the code for free.
The first think I would say is check trans fluid level. Need to make sure you know you check transmission fluid level while engine is running, emergency brake on and in Park. Best to have engine up to operating temperature. I always like to run through gears before put in park and check fluid level. I have known people who check transmission level with engine off that is the only reason I brought it up. If the engine is off you will have a higher level and think your fluid level is good.

https://www.youtube.com/watch?v=2ETvtt8fcr4

P0783 DODGE - 3-4 Shift Malfunction
Possible causes- Low transmission fluid level
- Dirty transmission fluid
- Faulty shifting solenoid valve
- Shifting solenoid valve harness or connectors
- Shifting solenoid valve circuit is open or shorted

run the fault codes and look for a sensor / servo fault for the torque converter clutch

When it comes to transmissions the home trouble shooter should be concerned with just a few things. Number 1 is fluid level. Start the truck and let it warm up to normal temperature. Then set the E-brake and place the transmission in Neutral. Check the fluid, if the fluid is low, fill it with the proper type of fluid. If fluid is ok, check any fuses and linkages corresponding to the transmission. If non of the above rings untrue you should take it to a specialist. Best of luck.

It's possible you have problems with 1 or more of the following:

1. Low level on transmission fluid - this isn't usually the case when you can't manually put a car in a gear but it's still worth investigating
2. Burned or old transmission fluid - same as above, not necessarily the main cause of a shift problem but could be a contributor
3. Linkage problem - over time, the linkage (connection between shift lever and transmission) can wear causing problems with "play" in the shift lever. A symptom of this is having trouble with the shift indicator lining up exactly on one of the selectors D,R,N,1,2,3.
   
4. Bad or worn neutral safety switch - car is designed to have foot on the brake when shifting gears. the neutral safety switch (attached to brake pedal) will prevent shifting if it doesn't sense a foot on the brake. ***

As far as checking the fluid level, with the car/truck running and in Park, look for your automatic transmission fluid filler tube. It resembles the engine oil tube only it's wider in diameter and is usually located lower in the engine compartment. It's location is customarily on the driver's side of the compartment, in front of both the power steering unit and/or the master cylinder reservoir. While vehicle is running, withdraw the dip stick, wipe it down and re-insert. Then withdraw the stick again and check the level. There should be indicators on the stick showing where the level should be. Another thing to check while the stick is out is the color of the fluid. Transmission fluid should be reddish or purple. Brown fluid is worn and won't perform as well as new fluid. Also, bad fluid often will give off a burned smell. This is another indication that the fluid/filter needs changing.

*** Most likely cause is #4 the neutral safety switch. If the fluid is bad it would be a good idea to change the fluid and filter regardless since it will adversely effect the performance of your transmission.

Sounds like you're low on transmission fluid. Let the car warm up and then check the transmission fluid while it is in neutral at idle while it is parked on a level surface (make sure the emergency brake is on of course). If it is low use only dealer fluid. Hyundai takes a special automatic transmission fluid and if mixed with a universal fluid can ruin their transmissions.

I’m happy to assist further over the phone at https://www.6ya.com/expert/cameron_6665f74c5d46fc23

No not your U-joints. They usually make noise when you shift in to gear or put on the gas in gear or let off the gas in gear when dirving. They would make a clunking noise.
Have you checked the Transmission fluid level? A low fluid level may cause hesitations. The fluid should be a nice bright redish color. If it is brownish and yucky looking it is time to change the filter and fluid.
Remember that the level marks on the dip stick are measured in pints and not quarts like the oil is. You need to put the emergency brake on and stick it in neutral and start the engine to check auotmotic transmissions. If it is low then fill it to the full mark. If any fluid at all shows on the stick then unless it is burnt and brown it is probably not your problem. If none showed on the stick you might get lucky. Keep me informed and I could use a thumbs up for me time please. The Raz Shack!!!

As far as I have found the 02 Isuzu Rodeo does not have a transmission fluid dipstick you have to in fact go under your vehicle to check, change and fill your transmission fluid. Transmission fluid level: You will have two plugs facing downward on the larger trans pan. The plug higher up on the pan is the fill/level check (stamped/recessed into the rear right corner of pan). ATF should just dribble from this plug on a hot, idling truck, in neutral on a level surface. The lower one is the drain. The one at the back of the pan in a recess is the filler. You need a hand pump or something similar to fill it to overflowing then top it off with the engine running. Make sure you shift through the gears a couple of times when topping off.

Before you put transmission fluid in, make sure it needs it. Check the transmission fluid with vehicle warm, engine running, emergency brake set and transmission in neutral. Pull the dipstick and wipe it off. Insert the dipstick back into the dipstick tube completely and then pull it back out. The fluid level should be between the two marks on the bottom of the dipstick. If it needs fluid pour the fluid into the dipstick tube (using a funnel). Only add about 1/2 quart of fluid at a time before you recheck it. Do not over fill the fluid.

check fluid level, make sure proper fluid is in transmission otherwise take to trans shop to diagnse if level and type is correct(check at idle normal operating temp)