Just a thought,
can you explain why a relay with no diode doesn't blow the fuse but the one with a diode ( knackered ) does?
It makes no logical sense to me as to why the fuse doesn't blow. I'm sure there is an explanation but my logical mind tells me that without the diode the fuse would blow probarbly quicker?
This is just out of interest.

Just to add, a diode conducts current on one direction only. In the case of a diode relay its wired such that it won't conduct current in the normal direction of flow when the relay coil is energised. It's purpose is only to quench (short out) the blip of reverse current (back emf) when the relay is de-energised, which can otherwise cause issues with sensitive electronics in modern cars - as you are now aware

As you can see therefore a diode relay must have its coil wired correctly to work without issue whereas with a plain relay it will work with coil current in either direction. All the factory fit relays in your car are diode ones as well.