SO's son's mom

My SO and I have been together for 6 years on and off. In one of our "offs" he conceived a child with another woman. Because we weren't together at the time, when we got back together, I welcomed his son with open arms. I consider him mine. The problem is, his sons mom is upset that him and I got back together. Since we have been together, she has stopped letting him see his son, stopped having communication with him, and has tried to cause problems between us. She is not providing a healthy environment for my stepson. She lives with her mother and father and two brothers in a very small house. They can't afford child care so they leave her little brother (3) and her son (14 months) with a 12 year old all day when they have jobs almost an hour away. My question is, would my SO have any chance of being awarded primary or full custody in court? We at least want joint custody.