Get your taxes done using TurboTax

there's nothing you can do unless you can get Congress to change the tax laws.  State and Federal laws differ in many aspects. The state court can grant full custody to parent A but allow the divorce or separation agreement to provide that parent A gets to claim in even years and parent B in odd years. The tax laws say differently. It's the custodial parent (CP) that gets to claim them in all years unless the CP gives the noncustodial parent (NCP) a signed form 8332 that must be included with the NCP's return. if the CP refuses the NCP can go back to court and the court can impose penalties on the CP for failure to comply with the agreement.  If the agreement does not provide for allowing the NCP to claim, then NCP can do nothing.