This IRS rules apply, regardless of what any custody agreement you may or may not have may say. Use the IRS tool at https://www.irs.gov/help/ita/whom-may-i-claim-as-a-dependent to see if you are the one legally entitled to claim them.
Basically, things dealing with divorce, separation and custody are handled by a judge below that of a federal judge. So regardless of what that lower judge may say, they can not over ride or negate the federal tax rules on this.
