My question involves child support in the State of: New York

My ex and I have a 6 year old. She broke up with me on our daughters second Christmas- two months after I caught her cheating on me with another man. Needless to say I was never willing to be without my daughter. I have paid monthly child support ever since. Our pay is about the same and we have our daughter the same amount of time. However my ex does have my daughter on her insurance ( she has dental and vision and I don't) so I'm more than happy to pay for that. I had been paying $250 a month plus extra if she had doctor visits or needed new clothing for school- even though I supply her with all her clothing and needs at my home as well. Over the years my ex wanted more and raised it to $470 a month and now now for the past year it's been $400. She threatens to take my child from me if I don't do as she says. I've calculated my child's expenses, minus food and clothing because we both provide that separately, and I am paying for almost everything. Money has been tight lately cause I moved out to keep my daughter in her school district because my ex wanted to move out of her mothers. She moved somewhere more cost efficient but the schools weren't as good. We have never been to court and had never been married. I want to know if going to court would help or hinder me and if there is anyway we can split my daughters costs 50:50 as well