Honestly, I couldn't see an issue. The green bar is your pet's HUNGER bar, while the RHAND and LHAND were just fine from what you showed on the video. All of the items you used were two-handed and were being held and shown on both hands, like they should. The bow is not shown in both, because LHAND is where ARROWs are shown.
Either way, the green bar is controlled from the java. Your server sends a packet to your client commanding it to show the green bar over your head. You would have to locate the enum/packet and remove it.