Pay and be done. I am not saying you have to give her 400 a month. But maybe you can figure out a way to give her something. Be creative. look at your assets. There are usually a lot of creative ways to make your x happy, but because emotions boil over we don't even try.
Well I was paying my X child support every month. In addition I was spending just under equal time with my child. However, one day my X car broke down. She asked me to help get her another one. I was like "are you out of your flaming flipping mind!" Biggest mistake I made. I could have easily scraped up 3,000 to help buy her a used car. I decided not to and found myself in a court battle that cost me 4 years of my life and my entire life savings... Wish I could go back in time to help buy another car.
After the legal fees you will pay and the amount of time in court, you may be better off paying her. Now if you simply cant afford then you don't have a choice. But if you can, you may want to swallow the crow and save your self some money.