How much wood wouldn’t a woodchuck chuck if a woodchuck could chuck woodn’t?
Enough already.  
I get it.  It is an easy mistake to make, misusing would and wouldn’t.  It happens to me all the time.
“Honey, when I said I didn’t see any reason why I would go to the ballet, I meant to say I couldn’t see any reason why I wouldn’t go to the ballet.   It’s not that I wouldn’t go to the ballet, I would.  But there is a poker game that night . . .”
It’s like a double triple negative head fake kind of thing. 
Of course I could just tell my wife that I have absolutely no interest in seeing the ballet.  But my wife has a way of convincing me otherwise.  She is pretty strong and powerful in her arguments.  
As someone who has learned the hard way when to defer to his spouse in order to preserve a more perfect union, you would think that I wouldn’t want to explain my position, even if I could.  Or maybe you wouldn’t think that I would want to explain my position.  I am not sure which way is correct. 
The point is, as someone who butchers the English language every time I open my mouth, I sometimes get confused using would and wouldn’t even though I really oughtn’t.  Maybe that qualifies me to be president.

I do have an excuse.  In college I took one English course.   English for Engineers 1.0.  The course was required to graduate. 
But given the recent brouhaha over would and wouldn’t, I decided to do a little research on the subject.  Very little. 
And I discovered knowing how and when to use would and wouldn’t is actually very simple in a grammatically over-complicated sort of way. 
To understand would, we have to start with will.  
The word will has many meanings and can be used as both a modal auxiliary verb and a noun.  For example, “if you don’t go to the ballet with me you will be cut out of the will and you will be sent to a gulag dog house in Siberia.”  
Will is only used in the present to describe things in the future, as in “I will live to regret it if I go to the poker game instead of the ballet with my wife.”  When the future rolls around I no longer will live to regret it because I am no longer alive to regret it.
And the word would is simply the past tense of will.  So if using will describes an expected action in the future, the past tense must describe an expected action in the present.  For example:  “If I were you I would think long and hard about whether you would rather play poker or go to the ballet.”  
Would can also be a conditional verb indicating events in the future based on certain conditions.  Like, “I would  go to the ballet if it wasn’t so boring.”
The same treatment applies to the negative.  Wouldn’t is a contraction for would not and willn’t (pronounced won’t) is the contraction for will not.  These words indicate a contrary action in the future even when referring to it in the past.   Thus, “I will not go to the ballet”.  And then further in the future, “I wouldn’t go to the ballet at first, but my wife changed my mind.”
To make matters more interesting, when dealing with would and wouldn’t we also have to deal with the have and have nots.  
When I say to my buddies, “I would have played poker, but my wife made me go to the ballet,” I am stating in the present my willingness in the past to do something which did not happen and was probably never going to happen and may never happen again.  That is, playing poker.
When I say to my wife, “I would play poker, unless you want me to go to the ballet”, I am implying a future action modified by a likely condition that is totally out of my control.  
Both are grammatically correct, but one plays a lot better than the other.
And what about will have been?  That is something called a perfect future continuous tense.  It is used to describe a highly likely event in the future, as in “at the end of the ballet I will have been watching leaping men in tights for over two hours without a drink.”
In summary, using would and wouldn’t is like using did and didn’t or right and wrong.
Intuitively, you just know.
Well, live and learn. I shan’t make that mistake again.
I am looking forward to the ballet.  It’s the Bolshoi.