|Cindy, the one with purple flowers does not belong to any of urushiol oil family of plants (poison ivy, poison sumac, or poison oak) as they all have whitish flowers. It is hard to say without seeing a picture of the other vine, but it sounds unlike them also.
Send me a pic if you can at firstname.lastname@example.org and I will try to identify your vines. I have done this for lots of people here. Please let me know what state you live in too, as some plants only grow in certain areas. Without actually seeing the plants I cannot say what species you have, however I know for certain the first one is not PI or it's relatives. Still, some people can be allergic to plants that ordinarily don't cause dermatitis. Take the cautious approach and always wear gloves when weeding or pulling up undesirable plants.