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My daughter's 01 Durango will not disarm when you unlock the doors. It is the OEM alarm system. It will arm with the remote but will not disarm when the unlock button is pressed on the remote.
To reset the factory alarm close all the doors and manually lock them. While outside your truck place the key in the drivers side door and turn the key all the way to the left then all the way to the right then to the middel position and open the door. Do not use the key FOB. You must do it just like this and the factory alarm will reset.
and check here lots of info on the OEM alarm system