The general strategy this is solved is through an MVC architecture. In an MVC architecture, you keep a model that represents the data being manipulated and is the single repository of truth. In some situations, this model may be linked with a database, but there does not necessarily have to be a database.
All of UI views only have to know about the model and how to update itself with regard to the current state of the model. All UI controls only have to know about the model and how to update the model when the UI control is activated. The model provides a notification service for interested parties, every time the model gets updated, the model searches through the list of interested parties for those that are listening for the type of change that had just happened, and send a change event notification so they can update themselves.
This way, any UI elements doesn't need to know about any other UI elements, it only needs to know about the models. Note that when a UI control is activated, it triggers action notifications to the model, which triggers change notifications to the UI views and possibly to the database; the UI views do not need to know what control originally triggered the change in the model and thus do not need the original action listener. Which controls triggered the change does not matter, only that the change happens and that the UI view is stale and need to be updated.
Note that a single UI widget can play the role of both a UI view and a UI controller, but these roles should be distinguished.
In your case, Child #1 seems to play the role of the UI controller, and Child #2 plays the role of one of the view that needs to be updated. You need a way to manage the events registrations such that the Model is notified when Child #1 is activated and register Child #2 as an interested party whenever the Model's status changes. Once this is set up, child #1 should only need to know to notify the Model that it wants the model to change its status to "Bye"; the Model then needs to look for who is interested in the status change, and find that Child #2 does, and sends a status change event.