For removing the paint entirely so you can try again, you can use oven cleaner, the white creamy kind that comes in a spraying can. Put some into a plastic container with a lid, put the painted part in, and spray more of the stuff all over it. Close container, leave until tomorrow, and rinse it off with a soft toothbrush under running water. Wear rubber gloves as you do all of this, though.
Alternatively, I've read that Dettol is also a good paint remover, but you need the original formula with the distinctive hospital smell. When I wanted to try this for myself, all I could find in the shop was a more modern type that didn't affect paint at all.