2001 Dodge Dakota right front break keeps hanging up

With the problem wheel off of the ground, try to spin it by hand, have some one apply the brake while spinning. Once the brake pedal is released, does the wheel spin freely?
This is not uncommon. You need to remove the caliper in question and make sure your brake pads aren't rusted or frozen in their "keepers." On some vehicles, rust can build up behind those stainless steel clips that the pads ride on and put pressure to where they won't move. You should be able to move the pads in and out freely when the caliper is not installed. Second, it may be a caliper itself sticking. You can use a large pair of channel locks with one pad laying on the piston (or pistons) to push it back in. It should be firm, but not binding.

This is caused by either the caliper piston seizing in its bore or the brake hose colapsing inside. remove the caliper and try to press the piston in with a c clamp. it should be very hard to move in according to your problem. now keep trying to press it in and crack the line at the caliper to allow some fluid to come out. if the piston moves now it is the line if not it is the caliper.