HEX is right on track. I have done front axle seals on both of my rams (2001 & 95).
Pull both axels, steering bar in front of diffy, and loosen the bearing caps, DO NOT TAKE THEM OFF, Notice the stamped markings already stamped on the caps.
I never did have luck using a pry bar myself, I will let you in on two different ideas that worked for me.
Use the two wrench method, Now you are ready to remove the differential. You will not be able grab it and pull it out with your bare hands. Get a 3/4" box end wrench and place it on one
of the ring gear bolts. Next, turn the pinion until the wrench contacts the top
of the axle housing. Turn the pinion more and the differential will be forced
out of the housing. Now is where you can grab it and remove it. If it is still
tight, use a pry bar or other kind of lever.
My favorite way to remove a carrier, use a paper towel. Thats right a paper towel, Take one sheet and fold it 3 or 4 times and feed it into the pinion/ring gear area and use a wrench and turn the carrier and it will walk its way right out of the housing. Its nice to have a helper, once loose hold carrier and take caps off, carrier is heavy so be ready.