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If your house is elevated and the crawlspace is under that elevation so as to be exposed to the outdoor air, then you are fine: install the insulation between the joists, with the vapor-barrier between the insulation and the interior or your house.
However, if your crawl space is underground or if it is insulated from the outdoor air, itself, then that vapor barrier could end up trapping moisture inside the crawl space, which could condense inside the insulation and rot it out. If that is the case, then either ripping out the current barrier or leaving it in could be the proper remedy. We can't tell from here.
Take a look at some of the other recent posts for the purpose of a vapor barrier to judge for yourself. There are also relevent posts under "Basements" on this Bulletin Board.