Danny's case is similar to an actual NY case from 1987 when a diplomat accused of beating his children could not be arrested because of diplomatic immunity. A court order was obtained for child protective services to remove his children, but the US Supreme Court ultimately ruled that this was illegal under international law and the children were returned.
When Jamie is talking to Eddie in the ladies locker room he puts his bag on the bench and when they walk out of the locker room he leaves it behind.