Well, in a nutshell, the problem is in the passenger door, probably the motor attached to the lock or the wiring to the passenger door.
Each lock actuator has five wires - two for the motor, and a switch with three wires - the common, the lock wire, and the unlock wire. Either lock or unlock is connected to the common, depending on the position of the actuator.
If either the lock or unlock wire is broken or the switch is faulty, the system will lock but not unlock or vice versa. I don't think this is your problem.
If the motor moves the lock (the lock pin inside the car can be seen to go down), but the switch doesn't go to the 'lock' position, then again the system will unlock. I don't think this is your problem either - your lock pin probably doesn't go down.
If the system tries to lock the passenger door and the actuator/door pin doesn't move, the switch will remain in the 'unlock' position - so, the system immediately unlocks the doors. I think this is what you have.
The fact that the system will lock when you use the key in the passenger door suggests that the passenger door actuator is not running or not moving the lock. The problem could be the motor (stripped gear inside, perhaps), its connection to the lock, or the wiring that runs into the door.
The GTV/Spider seems to use Alfa 164 door latches (designed in the 80's
). This is good news if you do need a new lock actuator, as it is a common design (plastic housing about 15cm long, mounted by two screws) and a new generic unit can be substituted easily. An auto electrician is the place to find this, or http://m.ebay.co.uk/itm/5-Wire-Car-D...730?nav=SEARCH
The one I have linked to should fit straight in, but some other recent designs of generic lock actuator have a swivelling head. This is longer, but in the worst case, you can attach a new rod (provided with the actuator) to the existing door lock rod for the pin inside the door. i.e. 'piggyback' the actuator onto this rather than onto the original linkage.
This last approach, by the way, is the economic option to repair newer cars that have their own custom designs of motorised latch (Alfa 166 for example) for which parts are £££/$$$.