What I hear you saying, Nyaanyaa, is that by asking, "how can I get my child to accept my criticism and take it on board?", the OP is already headed away from behavior change and useful communication. You would rather that (s)he instead ask, "how can I help my child develop his/her own internal barometer of how to behave in society, including how to react to criticism (from any source) without melting down?"

Is that right, or have I missed something?

Incidentally, the "sandwich" doesn't work for squat here, either.