Hello Ami:
No, parents who are kind, loving, and more importantly, mentally stable (which an NPD person is not), do not behave in the manner you describe.
Ordinary parents can, and do, get annoyed at times, which is quite normal, as they are only human. But they do not reject, humiliate, become emotionally absent, play mind games, or any of that kind of stuff.
Then again NPdisordered are unable to behave in any other way, it is a type of "coping mechanism", to give it a name. That is how THEY deal with life. It is hard to accept that, particularly in a parent (I would imagine. Because I had good, kind parents).
All the best Ami, and I hope you are feeling a little better each day
Hermes