Residencey- temporary absences - Count time that you or your child is away from home on a temporary absence due to a special circumstance as time lived with you. Examples of a special circumstance include illness, school attendance, business, vacation, military service, and detention in a juvenile facility.
However since the child has lived for more than a year with your ex and not with you, you will not be able to claim EIC for them. Your ex would qualify for the credit and so if he claims, you definitely do not stand a chance to get the credit.
Let me know if you have any question.
Please note: This advice is provided with the understanding that all the relevant facts have been provided by you. Any change in facts might affect the advice given and hence may not be relied on in such cases. Nothing contained in this reply was intended or written to be used, can be used by any taxpayer, or may be relied upon or used by any taxpayer for the purposes of avoiding penalties that may be imposed on the taxpayer under the Internal Revenue Code of 1986, as amended.