A woodgrain door has a thin woodgrain foil applied with adhesive - it's called foil but is just a thin plastic film.
Is it just the foil / film that has split?
You would really have to hit the frame hard to crack it.
Not sure there is an easy repair - if its just the foil then colouring the white PVC that is visable the same colour as the foil would hide the problem.
If it is actually cracked - I can't see a 3 year old being able to do this - then a new frame is really the only answer.