Replace with a second hand genuine part. Hold out for one in your own colour to save yourself the cost and pain of spraying and colour matching.
It's not worth repairing if it's as bad as you described - you should be able to pick up a decent 2nd hand wing for about £20-£30.
I'm guessing yours is a small bumper car, as on the big bumpers the splitter is attached to the bumper itself and slots into the plastic wheel arch.
If it is a small bumper car, then check the front valence is okay.