VAPGULFVET,
In your case, if it were me, I would attempt sanding it down, as much as possible without compromising detailing. ie: plastic trim, name, door handles, etc. If doing that doesn't seem to be working for you, here's what you can do; Mask the window openings, chrome bumbers, etc, and spray on a coat of Easy Off Oven Cleaner. The next day, WIPE off the old paint with a cloth until you are down to the bare plastic.
Now I know there are many procedures that will produce a great finish, here's the one that works for me, and can be accomplished with materials you can get from any good retail store:
1) Clean the plastic with light detergent & water and DON'T touch the bare plastic again unless you wear rubber gloves.
2) Using a can of Testors spray paint, make several light coats until a uniform color has been achieved, then cover the body with a box to prevent lint from getting on it. (light coats prevents build-ups.dripping)
3) After completely dry (at least two days), apply a coat of Testors Gloss Coat and allow to dry at least two days.
4) Apply any decals on the "slick" surface. (eliminates decal clouding)
5) Apply the second & final coat of Gloss Coat and allow to dry for at least four days.
6) Apply some type of cream wax in tiny amounts... (generally I rub a cloth of wax on something else, then rub the car down with the same rag. This way, you don't have to worry about caking it in the seams)
The result is a beautiful deep finish, where the decals will appear to be PART of the paint job, instead of stuck to it.
Example:
http://gunsagogo.org/allisonfinish.jpg
Like I said, there's many techniques, but this one works just fine, and uses materials that's readily available.
Take care,
Frank