Skoda Yeti Towcar

not an expert on these matters, but had similar problem with a Honda CRV, reversing and doing hill starts. I think you will find that the smell is the clutch plates/fluid getting very hot hence the foul smell. Be very careful it could lead to clutch burn out. Fit a mover could be cheaper than a new clutch.

Are your caravan's brakes adjusted correctly? ie are they collapsing when reversing as they should?

has the car got emergancy reverse braking working through the sensors. if it senses anything it is way it applies the brakes to stop you hitting something and may be doing it because the vans in its way so to speak. if not then would suspect clutch as stated earlier.

The only time I had clutch smell was reversing up a steep grass bank doing a 7 point turn after turning into wrong entrance. Certainly did not last all day though let alone all week.

Was this on a reasonably level area? 

yes CRV was terrible reversing on grass even with only a slight slope, was towing a Coachman 5 berth so it came in at 93 pct. Agree smell did not last for a week, but a mechanic told me that once the fluid was burnt it would smell for ever, and it did if you lifted the bonnet. CRV not good at hill starts either, was a manual box, got rid and bought an auto sorento brilliant, and fitted mover to van, solves most of the problems.

I have a similar Yeti and as I have with previous cars get the clutch smell when reversing caravan. Always put it down to my reversing rather than the car. Love the yeti and looking to replace with a 2lL 4 x4 before they become extinct in the new year.