carpet cleaning an rv

A bucket, scrub brush, and shop vac with an appropriate nozzle (the "claw tool" works pretty well) are a quite good facsimile of a proper carpet extractor, and in my experience much more convenient for tight corners. Plunge the brush in the bucket (warm water mixed with carpet detergent as per usual directions), scrub a bit of carpet so that it's fairly damp but not overflowing, and vacuum out the water and dirt. Another pass with rinse water will help get detergent residue out. At least on my steam vac, the hand tool is not especially effective, though the main carpet scrubber works nicely.

I wouldn't hesitate to clean the carpet for fear of water damage. Just get out what moisture you can, and take steps to help the rest to dry pretty quickly, such as opening windows, running a dehumidifier, or firing up the furnace or AC (depending on the weather and such).