Clive,
I must be lucky, having towed with Vauxhalls, Peugeots, Nissans and currently my 2nd VW with different mirrors to my 1st, I've used a number of different towing mirrors and never had a set that interfered with the glass of the car mirrors.
My last 2 sets of mirrors have been Milenco, the latest of which are the Aero, which I can recommend.
They are the type that have screw down clamps rather than the elastic straps and I've found them to be very secure.
It may be the design of your car mirrors, but with my towing mirrors in place, I can still move the glass in my car mirrors without the lugs interfering.
Ken.