Your understanding is correct. As the custodial parent (the children live with you for more than half the year), who pays more than half the household expenses for your home, you would be entitled to file as Head of Household and also claim EIC. The noncustodial parent ( your ex) can claim the Child Tax Credit in 2018, and the dependency exemptions in 2017. This law has not changed, so if your situation was the same in 2017, you would be able to file the same as in 2018. You should consider amending your 2017 return, but be careful making your entries, because people often make the mistake of claiming the dependents when that was not their intention.
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