I totally agree Graham, with what you have said, in that as soon as I 'let my insurance sort it out' I have started a claim with my own insurance company who will be accumulating costs from day 1.
If the other party decides to deny it or drag their heels then my ins co will be looking at me to reimburse them (via loss of my valuble no claims) as, in your case this could drag on forever or indeed never be settled.
That is why I (or my wife) will be sueing the other party direct, and as am am au fait with the small claims system that is exactly what I am going to do.

I am not going to use my insurance company and risk losing my no claims for something that was not our fault.

The question still remains then:

Who should sue, my wife as the driver or myself as the owner?

Cheers

Colin