If my ex-spouse claims my child as a dependent, can I still qualify for the Earned Income Credit (EIC) or Child and Dependent Care Credit?
It depends on the physical custody of the child.
If your child lived with you for more than half the year (the IRS usually counts the nights spent in your home), you can claim the Earned Income Credit and the Child and Dependent Care Credit. This is true even if your divorce decree allows your ex-spouse to claim your child as a dependent, or if you're allowing them to do so.
In cases of shared custody, it might be a good idea to keep track of the number nights your child stays with you.