I have looked through 1981 Census around Auckland and can't find any link that a David, Karen, Philip or Susan have with each other, It is possible that Karen or Susan had married and have different surnames by 1981.

My sugestion would be to find a death notice for Harold or Brenda which may show more deatils.

Can I ask where you got the children's names from, maybe that sorce has more info ?

I didn't find a Harold SMITH (no middle name) that died in the 1980's, I found 1x that was born on 13 January 1925 & died 1991.
https://www.bdmhistoricalrecords.dia.govt.nz/Search/Search.a...
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The cloest school I found to there house was "Howick Primary", I noticed there was a Philip SMITH did go to that school. http://www.oldfriends.co.nz/InstitutionPhotoView.aspx?id=497...
My gues is that the kids are about 10yrs old in that photo which may fit his age, If you join that site you can e-mail people at no charge. Try e-mailing others that were in his class, maybe they know where Philip is.. or ask if Philip had a brother or sister.

There is also a Philip SMITH who when to Howick Collage...
you could e-mail him here.
http://www.oldfriends.co.nz/MemberProfile.aspx?oldfriends_me...
As it happens, I know this Philip does not have a middle name. If you want more details on that Philip e-mail me jogregory@xtra.co.nz