You can amend for three years, unless there is a court order dated before 2009 or you gave him form 8332 (https://www.irs.gov/pub/irs-pdf/f8332.pdf) allowing him to claim the kids. You have until April 15, 2017 to amend 2013.
The
custodial parent has first priority on claiming the children on her taxes;
regardless of the amount of support provided by the non-custodial parent. The
non-custodial parent can only claim the child as a dependent if the custodial
parent gives permission (on form 8332) or if it's spelled out in a pre 2009
divorce decree. (without conditions - usually the
payment of child support).
There is a
special rule in the case of divorced & separated (including never married) parents.
When the non-custodial parent is claiming the child as a
dependent/exemption/child tax credit; the custodial parent is still allowed to
claim the same child for Earned Income Credit, Head of Household filing status,
and day care credit. This "splitting of the child" is not available
to parents who lived together at any time during the last 6 months of the year;
then only one of you can claim the child for any tax reasons. The tax benefits
may not be split in any other manner.
Note in particular
that the non-custodial parent can never claim the Earned Income Credit, Head of
Household filing status or the day care credit, based on that child,
even when the custodial parent has released the exemption to him.
So,
it's good idea to let the other parent know that you will be claiming those
items, as many first time divorced parents are not aware of this rule and may
try to claim those items, which will cause the IRS to send out letters.
Ref: http://www.irs.gov/publications/p17/ch03.html#en_US_2014_publink1000170897
The money you hear about people getting for just filing a
tax return claiming kids requires you to
have some earned income (wages or self employment). Without earned
income, you are not eligible for the "refundable" Earned Income
Credit or Additional Child Tax Credit.
