Do I have a chance getting joint custody of my son?

Long story short, my son, who is now 2 (almost 3) was conceived through a one night stand. I didn t know he even existed until the mother told me about him 6 months after he was born. I stepped up immediately to take care of my son and even tried to make it work with her, she didn t want to have a relationship with me.

Background information:
1. I'm a Plumber with a full-time job.
2. She is a policewoman who works in the family court.

Since the beginning, we decided on this:

- I paid half for his daycare
- Gave her a set amount of money every week

BUT in the beginning, I would have to ask to see my son and she wouldn't let me have him overnight. Now, she let's me have him overnight, but only for 2 days a week.

Recently, she comes to me asking for more money a week, because she can't afford her car insurance and mortgage… Why? Not sure, she makes more money than me! But I give into her because my son lives with her most of the time.

More recently, she asks for more money. Questioning her about this because now I can barely afford to give her more money, I agree to give her more money IF I can have my son more than 2 days a week. She says no and in fact says that she wants me to have him less… LESS! I don't know what I am doing wrong and have never done anything malicious to her, I don't understand!
Added (1). Since our disagreement, we are going to court. She is seeking full custody, I want joint. No reason to take him completely from his mother, but at the same time why is she trying to achieve that by taking him from me? Even worse, she works at the family court and knows everyone there and may even succeed.
Added (2). What should I do? I have saved all communications from her regarding the money that's she requested over the past few months, I love my son to death and have never hurt or mistreated him (or her!), work full time and have my own apartment.

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