Assuming your meet all the other eligibility requirements, you still qualify for the earned income tax credit while stationed abroad as active duty military.
As you work through the interview for the tax credit, the program will ask how long you lived in the U.S. Be sure you select 12 months. On the following page, check the box next to "Active duty Military stationed outside of the United States". After that, it should show that your children are qualifying children for EIC, and allow the credit.
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