The question, as posed, is
- Is it wrong to use “not” in sentences that have an “all…not” form?
and the answer, as far as I can reckon it, is that it's not.
It is never wrong to use not. If that's what you mean, of course.
I don't quite understand what you mean by sentences that have an “all…not” form,
but I don't imagine you do, either. Description of syntactic structures is hard.
What's going on in the example question
- All of the women in the district did not vote for the lone female candidate.
is that there is a quantifier (all) and a negative (not) in the same proposition,
and when that happens there occurs what is called a Quantifier-Negative Ambiguity.
That is, there are two possible ways in which the negative and the quantifier can interact.
Either it means
All Women (Not Vote X) [i.e, "All the women voted non-X"], or
Not (All Women Vote X) [i.e, "All the women voted X" is False -- someone voted non-X].
This ambiguity is likely and often unavoidable in all of the following environments:
because quantifiers, negatives, and modals are all logical operators which bind a focus.