Thank you for giving me the opportunity to assist you. I will give the best answer that I can with the information provided.
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.
Please let me know if you need additional information.