I found this but you may want to call the fence company. They should be able to tell you if this will work or if there is trick to removing it. A friend of mine used a pressure washer on her vinyl privacy fence that had a small section of paint on it. I'd try the pressure washer for sure though. You'd be surprised how much dirt, etc come off the fences and house siding with those.
Graffiti and Paint Remover Towels.... SCRUBS® Graffiti and Paint Remover Towels nonscratching, abrasive towels remove paint without redepositing on surfaces. Works on hard nonporous surfaces such as aluminum, steel, glass, vinyl, and more
A Magic Eraser might work, but it'll make the fence dull in the areas where you scrub.
As far as nail polish remover goes, be careful if you use 100% acetone; it may dissolve your fence too. But if it doesn't, you can buy it in big jugs from a hardware store (it'll be in the painting supplies aisle) ... it sounds like you'll need a lot of it, unfortunately.