The short answer is that you and your separated spouse will need to decide who claims the dependent amounts; provided:
1. Your separated spouse has not claimed the amount for the children. If you and your spouse can't decide on who will claim it, neither of you will get to claim it.
2. You and your separated spouse did not claim the spousal amount (the spouse for whom it was claimed would have to make less than 11,809 after taxes for it to be the case).
3. No one else in your household is claiming them as dependents.
4. You are not claiming support payments for the child. (If the dependent amount exceeds the support payment amount, then you can choose not to claim the support payments). If you're not sure, we recommend running both scenarios and choosing the one with the best outcome.
Let us know if this is helpful.