You create a button by going to the front panel and selecting a button style you like. If you were to change to an architecture based on the event structure, I'd say add a value change event for the button with a visible property inside the event. If you don't change it, just wire the Boolean to the visible property of the graph.
At some point, you really want to redesign the program. The use of multiple graphs stacked on top of each other is going to be a performance hit. Any one of your graphs can be used for displaying all of the plots.