Does the horn blow when you push the red button on the remote? If this is an OEM remote it only has door lock/unlock and alarm functions. If the horns blows every time, it may be a door lock issue, not a key fob problem.
Try cleaning the ground points. There is a small black box, in the engine compartment, attached to the fender wall, next to the ABS module. Remove the one attach bolt and clean the surfaces. There is a second ground, exactly the same type box, located on the fender wall behind the air filter case. Could also be a problem with the driver's door lock switch logic board.
Keep us posted.
Try cleaning the ground points. There is a small black box, in the engine compartment, attached to the fender wall, next to the ABS module. Remove the one attach bolt and clean the surfaces. There is a second ground, exactly the same type box, located on the fender wall behind the air filter case. Could also be a problem with the driver's door lock switch logic board.
Keep us posted.