Claiming dependents can be complicated, and just because someone else claimed them first doesn't mean you might not be the personal legally entitled. This is true in divorce and separation situations, but it can also be true with unmarried parents living together (where, if one person claims the children in the wrong way, they will prevent their partner from claiming the children but will also lose benefits themselves).
If you post more details about your situation we might be able to provide a better answer for your situation.
