I see a couple of issues with the code in your image. First, need to (re)load data in the Frm_OnNewHome
method. The current method does nothing after the notification so the bound data source will remain unchanged. Also, a SqlDependency stops automatically after it fires so you need to start it after each OnChange.
Below is the full working code from a test on my machine with the Save button implementation. I ran 2 instances of the application on the same box and SqlDependency.OnChange was fired whenever the Save button was clicked on either form. I added code for the Save button, which I didn't see in your code as well as error checking for a notification subscription error.