No-one

  1. No-one was quite sure whether this was at the through sadness or at the thought of losing the cake commission.

  2. No-one was quite sure whether this was through sadness or at the thought of losing the cake commission.

Which one is correct and why not the other?

  1. ‘at the through sadness’ makes no sense.
  2. is correct.

Are you confusing ‘through’ and ‘thorough’?
Here ‘through’ = because of