Whenever a sewing project is not going well the first thing to do is change the needle. (I just learned this in a sewing class. You are supposed to toss needles after you have used them for 4 hours.) Also be sure you have the right needle for sewing vinyl. If there is not a specific needle for vinyl try a jeans needle or try a needle that is made for material that slide (like chiffon).
Next make sure all your settings are correct. There is a setting on my machine, on the left side, for thicker fabric. Try changing that. Also try adjusting the length of your stitch.
We sewers tend to move the tension around a lot when there is an issue. In my class I learned that tension is the very last thing to change.
Hope one of these helps!