Florida
My ex is arguing that he is owed the tax credit this year (2009 tax return) because he has a job and I don't. I re-married in sept 2009 and have primary custody of our child.
Unless your divorce decree says that he gets to claim the child, federal tax law applies. (and in fact, all the IRS cares about is federal tax law).
It doesn't matter if you are working or not. You and your husband, on your joint return, get to claim the child unless your divorce decree says differently...and again, the IRS won't go by your divorce decree. The state court judge can punish you for not obeying the divorce decree, but the IRS doesn't care.