If there is a valid order from a NY court, it cannot be unilaterally changed except by a higher court. A "military power of attorney" is a stop-gap measure for service people who need someone to look after their affairs while they are deployed--it does not confer custody of children, even if the service person actually had an order granting custody.
Custody cannot be changed without a court order. If the prior order was from a New York court, it may specifically say that New York retains jurisdiction.
Sign up to receive a 5-part series of useful information and advice about child custody law.