get_terms Parent Tags

The parent argument should do what you are asking.

parent
(integer) Get direct children of this term (only terms whose explicit parent is this value). If 0 is passed, only top-level terms
are returned. Default is an empty string.

http://codex.wordpress.org/Function_Reference/get_terms

That is parent=14 should get all of the immediate children of term 14, but no grandchildren or great-grandchildren. If that is not working I have to assume that a plugin or something in your theme is interfering, or I have completely misunderstood your problem.