Not dying, or wrong player dying: Add a for each to the hosts event sheet for the health check.
for each peer
peer health <=0
Also, you should add some checks whether or not either of the players are allowed to control their elements, who knows, either of them could be dead while they are pressing the buttons
Also, I have found that container elements referencing not always work in a multiplayer scenario, so I give everything IDs and use those as references for peers tied objects.
Also, you have an AI calling the destroy, which is processed on peer and host, and only host processes the re-position.
Would be nicer, to have the peer and host process half, peer sent message waiting for re-positioning, wait for a signal from host for replacement ready, then continue to replace the peer and set visible etc.
A bit of ping pong to verify the next action