What are the chances of me gaining sole custody of my 2 year old son?

My ex and I ended our 11 year relationship on 6/21 (never married). We agreed to keep the doors of communication open and share him equally. We also agreed that due to the fact that our son was still small, we would not bring any of our dates or significant others around him until he's able to process it.

Here's the facts;

*we are not getting back together.

*he moved in with his mother until he could get on his feet and get his own place.

*he stayed with his mother for 2 weeks and proceeded to move in with his girlfriend.

* she lives in a NYCHA building and has 3 children.

* his name is not on her lease and he is not suppose to be staying there.

*on 7/21, i asked him to care for our son so that i would be able to attend a wake. He called me and informed me that he would be able to watch him. However he left my son with his girlfriend (in the projects) for what would've been 10 hours. Apparently,he had to go to work from 3pm to 1am. At no point & time did he contact me to inform me of any of this. When i got out of the wake I called to retrieve my son and he refused to tell me where he was.

*on his weekends with my son he has him sleeping in his girlfriends apartment. and my son comes home looking dazed and lost in his thoughts.

* prior to this incident, he just started daycare and I believe between the new changes at daycare, dad not being home anymore and the new girlfriend with the 3 kids.... it's all too much for him.

*my sons father is 29. he hasnt paid taxes since he was 17. he pretty much lives out of laundry bags and floats from place to place.

What are my chance of gaining sole custody? I filed an order for custody and he has petitioned me for Joint custody. I have my own apartment. My son has his own room. I work full time,pay taxes and am able to provide for our child. I am stable and I want my son to be in a safe stable enviornment when he is with is father. I believe my son is being affected by his father's actions. His father blames his behavior on daycare. I believe it's a bit of both.

What are your thoughts?

Just wanted to add...

* he does not have my permission to have my child over there.

* i want him to have visitation but i do not want him sleeping over.