If you decide to strip the paint off and start again try this method and you should be OK.
Primer the car with plastic primer, any colour will do, leave it a day or two to let it harden and sand it if needed, then give it a coat of satin black, this will kill any red showing itself again, again leave it for a day or two then 1 dust coat of grey primer followed by white primer, you don't need to put loads on, just enough to cover the car, again leave it to cure then start dusting coat after coat of your white top coat until you get a good even coverage, leave it for at least a week for all of the paint to cure, hopefully by then you shouldn't see any more of the base plastic colour showing through.
Red and yellow are the two worst colours for plastic to paint over unless you want it the same colour of course.
I hope this helps you out, its always worked for me in the past.
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