Before I get too involved here you should take some time to look over these sites: the first deals with just basic crawlspace science (
crawl_spaces (http://www.solutionsiec.com/crawl_space_science.html - broken link)) and the second is an independent "
national resource that focuses on industrial process technologies, motors and drives testing, and applied building science" (http://www.crawlspaces.org/). Oh, you may want to look over a free blog by one specialist too that will illustrate some of the things they have run into (what works and doesn't, etc.). This may have some information that will help. (American Basement Solutions).
I've been in the indoor air quality industry for over seventeen years and I can tell you that just laying plastic over the ground of a crawl space like the one you're describing here doesn't always remove moisture and prevent microorganism and pest infestations. Making sure there is enough space between the ground and the crawlspace ceiling is important; making sure water is migrated away from the crawlspace is important; controlling thermal and latent properties is important (temperature and humidity) year round; and removing infested building materials is important - all for many reasons (too much to go into here).
I've seen a lot of people lay plastic down, open a couple of vents, and/or put in improper ventillation systems just to have more problems (both with pollutants and with building integrity). Whomever you've had there already may be able to give you more specifics on your crawl? If you're like me you don't like to have to keep going over one area of the house over and over again when there are other areas you want to get to. (I'm working on remodeling my home now.) I'd just hate to hear that that happened to you.
Look over those sites and consider having your previous contractor discuss with you some of the specifics. Each home is different and located in a different area with different requirements. Maybe once you've spoken to them you'll be able to get a lot of the work done yourself?