"Would have not" vs. "would not have"

• That would not have happened if John had completed his work.

• That would have not happened if John had completed his work.

The former seems correct. The latter doesn't seem incorrect.

Are there any cases where one ought to use the latter instead of the former?

The latter seems very wrong to me. Putting the word "not" after "should have" may possibly be correct form in other languages, but seems to me to be incorrect in American English. Also, I'm no English professor; but I would question the use of a comma in that sentence.

Well, in my opinion when we say "I would not like to know him" the word "not" makes the verb "to like" negative but when we say "I would like not to know him" the word "not" makes the verb "to know" negative. These are different situations.