I HAVE A 98 DURANGO AND EVERY TIME I TURN RIGHT AN APPLEY BRAKES THE ABS KICKS IN.

The master cylinder is pretty old (1998) and loss of Brake pressure equalization will affect ABS function

Firast you need to have the ABS control module scanned for the fault code that is set when the light is on, then work from that fault code.

i have a 98 durango 5.9 4x4 ive issues with the abs and brake light popping up off and on it is now happening more frequently especially when its raining, recently i replaced my abs module, calipers,pads, brake hoses and rotors the light discontinued popping up for about a week or so but its at it again and doesnt want to go away. before i replaced rotors brakes etc. i had an issue with my front passenger wheel rolling a little bit of white smoke out it heated up the rotors and everything else pretty good i think it may have caused the abs wheel speed sensor to start malifunctioning, i would appreciate any opinions or in put if possible

are there anymore symptoms? this could range from an idle air control module to a bad battery, does it stall right after a cold start or while idling at a stop?

Check for disconnected ABS sensors. The front sensors in the front are located next to the axle shafts. The rear sensor is located on the rear differential housing itself on top, in the middle. The ABS is monitored by the computer for performance. The ABS kicks on when the vehicle comes from a certain speed to a dead stop, keeping the wheels from locking up. That could be the reason for the speedometer not working. Or it could be a bad speed sensor. Both can also trigger the check engine light because it is monitored by the computer. The brake light usually comes on due to low fluid level. It can trigger the light, but not be low enough to impact brake performance. I hope this helps.

If you can feel the pedal pulsating and the light turns on the Abs is doin its job. if you want a better stop you could try a brake pad upgrade to ceramic pads and for even more stoping power add an after market drilled and sloted rotors.

You may have a bad wheel speed sensor.

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most likely... but you may just have a bad wheel speed sensor, get the abs scanned and it will point you in the right direction.

YOU NEED TO REPLACE THE PROPORTIONING VALVE!!
DOES IT HAVE ABS BRAKES ON THE FRONT? (MOST DURANGOS ONLY HAVE ABS ON REAR ONLY)

You need to put a scanner on the ABS system. See if it can be done for free at Advance Auto or maybe Pep Boys.