What is the call when player R purposly pushes her hand/fist into the net and contacts the ball, when the ball is hit into the net from the other side? Could this be unsportsmanlike?

DB

I have never seen that, and would probably need to see it to help out. My guess is, if you think she did it out of frustration, warn her. If it was a repeat act, or she was doing it for an unsportsmanlike reason, card her.

Our association discussed this indepth a few days ago. If the action was deamed to be intentional call a net violation. A player pushing or attempting to direct the ball through the net down to the floor, isn't allowing the game to proceed in the appropriate way.

SH

net
 

This has happened several times in matches I have called. Most of the time its when the served ball comes into the net. Nothing is done at that time.
I did have it happen once when I called a net violation. There was a high bad pass to the net falling right at the top and rolling just below the top tape pushing the net forward. The R team front row player contacts the ball (not in a block) just by pushing the ball through the net and deflects it. The S team setter was under the net ready to play the ball and because the R player defected it - I call a net violation on the R player. Point to the serving team.
So in reply to your question - It should be a judgement call if someone could have played the ball before it touched the floor.