Caravans and camper vans invariably have carpets made from manmade materials. Usually Nylon, Polypropylene or Polyester. They also suffer very heavy wear. A lot of the dirt will be dry dirt and pre-vacing with a decent vacuum cleaner will remove a lot of this dry dirt. This would be much better than relying on the limited power of your Numatic to flush it out.
It may also be the case that your pump may not be operating efficiently therefore not putting down enough fluid to flush out the dirt.
There are any number of chemicals suitable for the job, I would have a peruse at some sites to see what is available from the likes of Prochem.
Also bare in mind that manmade fibres do suffer abrasion especially in confined areas like caravans. Once this occurs it is hard to get a satisfactory result.