My ex-husband claims my duaghter for a dependent but does not qualify to recieve the EIC because his income is too high. She lives with me 12 months of the year along with my other daughter who I claim for a dependant and recieve EIC for. Can I claim EIC for child 2 if I don't claim her as a dependent?

Julie

Q: If the noncustodial parent receives permission from the custodial parent to claim a child on his or her tax return, is the noncustodial parent eligible for the Earned Income Credit?

A: The noncustodial parent cannot claim the Earned Income Credit on the basis of that child, because the child didn't live with that parent. The custodial parent may be able to claim the Earned Income Credit. A qualifying child for the Earned Income Credit doesn�t need to be a dependent.
Source: http://taxation.lawyers.com/Earned-Income-Credit-FAQs.html#four
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If your ex-spouse claims your child as a dependent, can you still qualify for the earned income credit or child and dependent care credit?
If you are the parent who had custody of your child for the greater part of the year, then you can claim the earned income credit or child and dependent care credit even if your divorce decree allows your ex-spouse to claim your child as a dependent or if you are allowing your ex-spouse to claim your child as a dependent.
Source: http://www.webtaxcenter.com/dependent_faqs.html
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http://www.irs.gov/ - This should answer most of your questions.