Yes, from what you described, your wife would be entitled to
claim the exemption.
Since the child was with your wife for the majority of the
time (when she lived with you and
when she lived with the father) she would be the custodial parent, and would be
entitled to claim her.
There could be an issue if the father claims the child on his
tax return, because the child lived with you and your wife for a period of time
and with your wife and the father for the rest of the year. It would be wise to
make sure that the father does not intend to claim the exemption on his return,
if only to avoid the complications that arise when two people claim the same
exemption. NC law regarding paternity wouldn’t apply on your federal taxes. You should make sure that you enter that the child lived with your wife the whole year when you are asked how many months the child lived with you, because she was born in 2017.
Your wife, as the custodial parent, could agree to let the father claim the child on his return by signing
Form 8332 or a similar
document waiving her right to claim her.
Since you were still married at the end of 2017, you can
file Married, Filing Jointly this one last time. It’s almost always the most advantageous
filing status. Filing jointly and claiming all three dependents would likely result
in the lowest taxes for you and your wife.
Please see this link to the Rules
for Claiming a Dependent on Your Tax Return.
[Edit 1/17/18 9:10 AM]
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