How to minimize only a few key residues' orientation

Generally, you would want to use a MoveMapFactory (or MoveMap) to select the residues of interest, pass that to to the MinMover, and use cartesian miminimization and a cartesian scorefxn. https://www.rosettacommons.org/docs/latest/scripting_documentation/RosettaScripts/RosettaScripts#rosettascript-sections_move_map_factories

 You would need to do this via RosettaScripts OR PyRosetta.  If you don't set the MinMover to use cartesian, you will get downstream movement.  https://www.rosettacommons.org/docs/latest/scripting_documentation/RosettaScripts/xsd/mover_MinMover_type

This script I wrote gives an example of this: https://github.com/SchiefLab/Jade/blob/master/database/rosetta/xml_scripts/design_focus_basic.xml

Here, it basically miminizes the 'focus' - IE the design residues, while packing the surrounding residues - 'nbrhood' in FastRelax. It has a few SimpleMetrics to report energetic changes between this.  In this script, I then design the focus in the same way.  https://www.rosettacommons.org/docs/latest/scripting_documentation/RosettaScripts/RosettaScripts#rosettascript-sections_simple_metrics

The idea is that I do the same minimization to the input as the design - so the energetic differences are more correct - IE NOT artifacts from the minimization.  Hope this helps to give you a starting point. 

-Jared