RUMOR: The 14th Amendment guarantees citizenship to children born to parents illegally in the U.S. Critics argue that automatic birthright citizenship could be changed by revoking the statute. Others say it would require a constitutional amendment because they believe the 14th Amendment requires birthright citizenship.
Answer: Each child can only be claimed as a dependent by one parent (except when married couples file taxes jointly). Typically, in the case of divorced, separated, or never married parents, it is the custodial parent who is legally able to claim a child as a dependent for tax purposes.
Since both parents above can legally claim their children on taxes due to the joint custody agreement, the parent who is waiving his right to claim the children for the year will need to sign form 8332, or similar statement, releasing the exemption to the filing parent.