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As far as the IRS is concerned, the custodial parent is the one who can claim the child as a dependent.  And since you are married to their mom, as a step parent you have the same standing to claim the child.  If the two of you file a joint return, you can claim the child(ren) as dependents on your tax return UNLESS your spouse signed Form 8332.  As you already know, it takes that form to allow the non-custodial parent to claim the child,  Even IF a 8332 is signed, the non-custodial parent can only get the child tax credit for the child.  The custodial parent still retains the right to earned income credit and the childcare credit.  

The ex's attorney is blustering--the IRS and the tax laws favor you and your spouse.

**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**