There is several things you should use when stitching vinyl, treat it the same as leather. The main issue usually is getting the feed dogs to grip and move it through; this is why there are commercial grade machines specifically for leather hides and fur etc, it is tricky to stitch.To stitch on a domestic machine, you need a leather needle with a spear tip to cut the leather so it doesn't split. Also, if you can get one, use a roller foot to roll over the fabric, or a teflon foot if you can't find a roller one. Also, use paper clips rather than pins to hold raw edges together (remove as they approach the foot and needle). You may also need to bash seams open after stitching (rubber mallet) and glue down the raw edges, this is how leather hides are stitched professionally. If you have to join more than 2 layers ie crossing seams, you'll probably need a Jeans-a-ma-jig device to help with feeding through the thickness and still getting feed. Like this
http://www.punchwithjudy.com.au/shop/jean-a-ma-jig.html You don't say what it is actually doing, ie stitches not catching, or the feed dogs not moving it through? But if it is an entry level machine, it may not have sufficient engine power to pierce the vinyl, especially if the textile is thick. Also, don't try to use a heavier thread than normal weight, if you want the stitching to look heavier, then just run two reels of thread through all the thread guides, tension and the needle eye together. Something like buttonhole twist will be too heavy for the bobbin tension and top tension to handle.Hope that this helps you with your project.