To sync an input value, you usually want to use the "Add client input value" and "Set client state" actions. This is one way to the host.
"Sync object" is generally used to update peers with information regarding position and creation and deletion of objects on the host. You can optionally also choose instance variables to sync with the "Sync instance variable" action. Again this is one way - peers will sync with a change on the host.
Peers should not change their objects to send to the host, as you describe. Peers send their inputs to the host, who makes the change on the proper object based on the peer input. That object then gets synced with all the peers.