I have been in a verbally abusive relationship for 8 years... he is bipolar. We live together but aren't married.
We have a 4 year old son together who is very loved. Often when we have full blown fights he says he is going to court. He is always trying to convince me that I'm an unfit mother (usually screaming this at me with our son watching). The problem is a couple of days ago I ran into a store for a moment and left my son in the car with it running and the a/c on. I regretted it as soon as I did it and felt horribly guilty. I had never even considered doing anything like that before. Well someone had called the police and even though I came out right after and drove off with him... the police showed up at my door an hour later. I could have not felt like a worse mother! Well they wrote up a report and then said he looked fine and healthy so gave me a warning and left. Now my boyfriend is so furious and using this incident against me. I understand him being mad, I would too... but he is bringing up every other problem in the world and blaming me for it (which is normal for him).

I'm trying to get up the courage to leave him but with out any money it's not going to be easy. I have been a stay at home mom since my son's birth so I have no money on my own.

My question is how bad will the incident with the police affect my custody of him. I know without a doubt that I am in his best interest. But will the courts? Does he even have rights since we're not married? Sorry for the long winded details.

His rights will be determined by the paternity establishment. If he has paternity established already, he as as much right as you do. Otherwise he would first have to establish paternity through the court.

I'll be honest - there is no way to determine what the court will factor in to custody determination. "Best interest of the child" is very objective and can always go either way.

I have heard a lot of cases similar to this one though and in relationships involving abuse such as yours, the threat is usually a control measure rather than an actual desire to be the custodial parent.

If this was an isolated incident, it shouldn't have a major affect. Also, I think doing this with a 4 yr old is not as bad as a younger child.

Since you are a stay at home mom, your bonding with the child will probably take precedence.