Beat 'em up style game.

OK so the game I'm making is a 8bit beat 'em up style game. It stars Pee Wee Herman battling his way through the decade. As the first level starts the player enters the frame in a path movement, then stops. A few second later, the enemies enter th frame and stop. The player's controls activate and you're able to move. The enemie all have a collisio box around them. When the player' s collision box comes into contact with the enemy's, the enemy will start moving towards the player. When the box's no longer overlap, the enemy stops. Another collision box is at the left and right of both the enemy and player. Say the player's left overlap the enemy's right, the enemy stops. When they no longer overlap the enemy will start to move again. Now lefts say the player is moving left while the enemy is stopped. The enemy will remain in the stopped position but will glide the direction the player is moving as if being pushed. How would i fix that?