OK... new idea... forget the electricals they are working right. The reason you kill the car when you put the relay in is that you have a massive mixture problem. I knew something was wrong with the ability to run after the fuel pump shut off. It isn't running on residual pressure, it is running after the motor throws off all the extra fuel once the pump is off and has cranked a while.
You should pull one injector from the motor with the line attached, run the fuel pump. There should be no fuel flowing from the injector (with engine not running). If there is then you are massively out of adjustment or the piston is stuck up in the fuel distributor.
Your plugs are probably soaked and you should change the oil.
Once you have the thing cleaned up try cranking and adding the relay. The idea is to introduce fuel when not running and see how it reacts. Do you know how to do a base adjustment of fuel mixture?
Bosch Master, ASE Master, L1
33 years MB technician