EmoteWheel.cs Snippet: Created by another team member, I took their code and changed it to work in a network environment, sending the emotes between clients through the server.

EmoteWheel.cs

public void ButtonAction()
    {
        buttons[CurMenuItem].sceneimage.color = buttons[CurMenuItem].PressedColor;
		GameObject Player = this.transform.parent.gameObject;
		NetworkInstanceId netID = Player.GetComponent<NetworkIdentity>().netId;
		Debug.Log ("Sending emote with networkID: " + netID.ToString());
        Vector3 offset = new Vector3(0.0f, 2.5f, 0.0f);
        //IconObject DisplayEmote;
        if (CurMenuItem == 0)
        {
			SendEmoteMessageAndClientID m = new SendEmoteMessageAndClientID();
			m.emoteType = 0;
			m.netId = netID;
			NetworkManager.singleton.client.Send (LevelMsgType.EmoteSingleSender, m);
        }
        else if (CurMenuItem == 1)
        {
			SendEmoteMessageAndClientID m = new SendEmoteMessageAndClientID();
			m.emoteType = 1;
			m.netId = netID;
			NetworkManager.singleton.client.Send (LevelMsgType.EmoteSingleSender, m);
        }
        else if (CurMenuItem == 2)
        {
			SendEmoteMessageAndClientID m = new SendEmoteMessageAndClientID();
			m.emoteType = 2;
			m.netId = netID;
			NetworkManager.singleton.client.Send (LevelMsgType.EmoteSingleSender, m);
        }
        else if (CurMenuItem == 3)
        {
			SendEmoteMessageAndClientID m = new SendEmoteMessageAndClientID();
			m.emoteType = 3;
			m.netId = netID;
			NetworkManager.singleton.client.Send (LevelMsgType.EmoteSingleSender, m);
        }

        menuon = false;
    }
}


public class IconObject : MonoBehaviour
{

	public void GetSprite(Sprite z)
	{
		//Emotetype = z;

	}
	public GameObject EmotePicture;
	GameObject Player;
	Vector3 offset = new Vector3(0.0f, 2.5f, 0.0f);
	// public Sprite Emotetype;
	// SpriteRenderer SR;
	NetworkInstanceId NetID;

	public float lifetime = 2.0f;

	public void PlayerNetID (NetworkInstanceId netId)
	{
		NetID = netId;
		Player = ClientScene.FindLocalObject(NetID);
	}