I understand. Yes, you certainly have a claim for child support, and perhaps even spousal support. However he is going to say that he's already supporting you and the child by giving you a place to live and other monies too. Your problem is that you have no power in this relationship with him.
The property division is a separate issue. If you can claim that you separated more recently then you have a better claim. Despite the divorce, you essentially reconciled afterwards and had a child together.
You need to decide that you're willing to change everything about your current life and lifestyle. If you take him to court then you may well decide that you can't or shouldn't stay in that house. You're only there while he's okay with it because there's no lease and you don't pay anything at this point.
It seems clear to me that your ex believes he's better off with this arrangement. Perhaps he's looked at what he'd have to pay you in child support, and he'd rather put you up in his cousin's home.
You should start by going to the nearest courthouse and finding the family duty counsel to ask more specific questions about the forms you'll need to get started if you choose to do so. If you get the paperwork started, see what's involved, and learn more about the process, you'll be in a better position to decide when and how to proceed. If you can hire a lawyer then I strongly recommend that you do, start with a face to face appointment to discuss these issues and get their recommendations. It's easy for me to say "take him to court", but you have consider the consequences of that decision for yourself and your child. Things might be okay at this point, but you don't have any custodial authority for when things have to change.
Does that make sense? Please reply with your questions and comments.