Window 1 will not be functional until the ModalDialog is not closed. Hence, call the instance of the 3rd window immediately after the following code in your base window -
var win1=window.showModalDialog("Child_Window 1.html",base_win,"dialogHeight:500px;dialogWidth:500px;dialogLeft:300");
Once the ModalDialog is closed, base window will call for the focus of your desirable window.