have you tried stitching it? it will probably soften up when it gets washed...another good reason for pre=washing i guess. but i would try and see how hard it's going to be to stitch by hand, if it is difficult then either take it off and wash it or switch to a different fabric....another thought...and you may want to call the shop and ask...we have one shop that carries some vinyl's...for picnic quilts, outdoor table clothes, could you have purchased something that is in fact 'plastic'?
good luck...i hate it when i have these problems...and i've had some pretty ... weird fabric issues