Coach assist
 

Despite my repeating "that's only two strikes, batter," batter continues towards dugout. Coach physically prevents her from entering the dugout and sends her back to the plate. The coach is not physically assisting a runner, so what do we have?

Nothing, put the batter back at bat. Even if they had entered the dugout you still have nothing, bring the batter back to complete the at bat. The rule regarding entering the dugout applies to runners and batter/runners who have completed their at bat. In your situation you have a batter, no rule about a batter entering the dugout.

Coach assist does not apply.

Abandonment does not apply.

The only rule you MIGHT apply (and you better have a great reason, and be prepared for the backlash) is the time between pitches rule for strike three.