New here. Here is my story.

[MoveFrwd]

First, pull this crap down from Facebook if you havent already. Pleading to thew "jury of your peers" is no way to earn her love. Even if her friends did see it and talk to her, it would need build any love between the two of you. You may as well learn now that you cant convince her of anything right now. There is no "being right" anymore. Trying to "justify" and "defend" yourself will only push her away.

So, I think it's time for me to stop being so vague seeing as how a lot of people on here are my friends.
My wife and I split up 2 months ago. Long story short, I had fallen into a really deep depression that lasted for two years and, in that time, I turned into an [censored], became someone she didn't recognize and neglected my family.

OK. So what are your goals and plans to fix this?

After a long time of this, she couldn't take it anymore so she took my son and she left.
We were still pretty much together, just not living together. We were trying to work things out and I was feeling better and better and finally starting to get over this 2-year slump through therapy etc.
Then, last week, I spanked my son because he threw food in my face and was acting out, and my wife absolutely flipped. Because, obviously if a father spanks his son he is abusive.

Im not going to discuss parenting styles.
But she didnt leave because you spanked your child once.

The way I read this, you had been draining her "love tank" for years, and this act pulled the last drop out. So, I wouldnt focus specifically on THIS incident, but rather look for the patterns that caused the tank to get so low.

Note that now is NOT the time to start trying to refill her love tank. Now is the time to learn HOW to fill other people's tanks. Any attempts you make for her will be seen as pursuing and will be rejected,

So now, she won't even speak to me.
She says she's trying to "distance" from me - which basically means she's trying to make it easier to move on from me.

Baloney.
If she wants distance, give it to her. Trying to close the gap will only push her further away.Do you think chasing after her will make it harder for her to "move on"?

She says that I basically proved to her that no matter how well I do and for how long, I always have it in me to flip without warning.
She has made herself believe that I am an abusive man and that she escaped from an abusive relationship.

Time to look inside. Not saying you are or were abusive. But what would cause her to feel that way. If she feels it then, it is valid. The key is to look at your behaviors and consider whether you think they should be changed.