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The rules for EIC state that you cannot qualify for the credit if one or both of you are a nonresident alien for any part of the year UNLESS you file married jointly and choose to treat your spouse as a resident alien for the entire year. (this means you must report spouse's worldwide income on the return).
Page 6: http://www.irs.gov/pub/irs-pdf/p596.pdf
You should also be eligible for the additional child tax credit presuming you have the income needed for the credit.
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