Your nieces & nephew would only be your daughter's first cousins. First cousins are not closely related enough for the children to be "Qualifying Child" dependents. However if they have been placed, with her, as "foster children", by a court or government agency, a foster child is considered closely related.
The closely related taxpayer that gets to claim the child is the one the child lived with most of the year. If you all live together, you may decide between you who will claim the child. If you can't agree, it's the taxpayer with the higher income (AGI).
There is no such thing as half & half custody.
