R Shiny - How do I toggle between two different plots using an action button

In my app, I want plot1 to display by default, and then if an action button is clicked, have plot2 replace plot1. If it is clicked again, revert to plot1, and so on.

server <- function(input, output, session) {
     plot1 <- (defined here)
     plot2 <- (defined here)
  
     which_graph <- reactive({
        if (input$actionbutton == 1) return(plot1)
        if (input$actionbutton == 2) return(plot2)
      })
    
     output$plot <- renderPlot({   
        which_graph()
    
      }) 
} 

You can create a reactiveValue and use an actioButton to toggle that value. For example

library(shiny)

ui <- fluidPage(
  plotOutput("plot"),
  actionButton("button", "Click")
)

server <- function(input, output, session) {
  whichplot <- reactiveVal(TRUE)
  plot1 <- ggplot(mtcars) + aes(mpg, cyl) + geom_point()
  plot2 <- ggplot(mtcars) + aes(hp, disp) + geom_point()
  
  observeEvent(input$button, {
    whichplot(!whichplot())
  })
  
  which_graph <- reactive({
    if (whichplot()) {
      plot1
    } else {
      plot2
    }
  })
  
  output$plot <- renderPlot({   
    which_graph()
  }) 
}

shinyApp(ui, server)

Here whichplot starts off as TRUE and then evertime you press the actionButton it toggles between TRUE/FALSE. This way you are not changing the value of the actionButton; you are just updating state each time it's pressed.

If your plots need any input from the user, you can make them reactive as well

ui <- fluidPage(
  selectInput("column", "Column", choices=names(mtcars)),
  plotOutput("plot"),
  actionButton("button", "Click")
)
server <- function(input, output, session) {
  whichplot <- reactiveVal(TRUE)
  plot1 <- reactive({ggplot(mtcars) + aes(mpg, .data[[input$column]]) + geom_point()})
  plot2 <- reactive({ggplot(mtcars) + aes(.data[[input$column]], disp) + geom_point()})
  
  observeEvent(input$button, {
    whichplot(!whichplot())
  })
  
  which_graph <- reactive({
    if (whichplot()) {
      plot1()
    } else {
      plot2()
    }
  })
  
  output$plot <- renderPlot({   
    which_graph()
  }) 
}