I am using the DT package to display a data table in my shiny app. Since I provide different data sets, I have radio buttons to select them and the data table updates automatically. 
What I would like to do is to preselect the available rows from df1 in df2 when switching the datasets. At the moment, my selection always get erased. When I try to save the selected rows (uncomment the two rows), my table get reset directly. 
library(shiny)
library(DT)
df1 <- data.frame(names=letters,
                  values=1:26)
df2 <- data.frame(names=letters,
                  values=(1:26)*2)[seq(1,26,2),]
ui <- shinyUI(
  fluidPage(
    sidebarLayout(
      sidebarPanel(
        radioButtons("dataset", label=h5("Select dataset"),
                     choices=list("df1"='df1',
                                  "df2"='df2'),
                     selected='df1', inline=TRUE)
      ),
      mainPanel(
        DT::dataTableOutput("name_table")
      )
    )
  )
)
Server side...
server <- function(input, output, session) {
  getDataset <- reactive({
    result <- list()
    result[['dataset']] <- switch(input$dataset,
                     'df1'=df1,
                     'df2'=df2)
    # result[['selection']] <- 
    #   as.numeric(input$name_table_rows_selected)
    return(result)
  })
  output$name_table <- DT::renderDataTable({
    DT::datatable(getDataset()[['dataset']],
                  options=list(pageLength=5))
  })
  name_proxy = DT::dataTableProxy('name_table')
}
shinyApp(ui, server)
I used the DT table, since I need the proxy and some interaction with the data table.
You can save selected rows only when going to change df like
server <- function(input, output, session) {
  dd=reactiveValues(select=NULL)
  observeEvent(input$dataset,{
    dd$select=as.numeric(isolate(input$name_table_rows_selected))
   })
  getDataset <- reactive({
    result <- list()
    result[['dataset']] <- switch(input$dataset,
                                  'df1'=df1,
                                  'df2'=df2)
    return(result)
  })
  output$name_table <- DT::renderDataTable({
    DT::datatable(getDataset()[['dataset']],
                  options=list(pageLength=5),
                  selection = list(mode = 'multiple', selected =dd$select  )
    )
  })
  name_proxy = DT::dataTableProxy('name_table')
}
shinyApp(ui, server)
Or a bit modification of @drmariod variant: use eventReactive instead of reactive
server <- function(input, output, session) {
  getDataset <- eventReactive(input$dataset,{
    result <- list()
    result[['dataset']] <- switch(input$dataset,
                                  'df1'=df1,
                                  'df2'=df2)
    result[['selection']] <- testing()
    return(result)
  })
  testing <- function() {
    list(selected=as.numeric(input$name_table_rows_selected))
  } 
  output$name_table <- DT::renderDataTable({
    DT::datatable(getDataset()[['dataset']],
                  options=list(pageLength=5),
                  selection=getDataset()[['selection']])
  })
  name_proxy = DT::dataTableProxy('name_table')
}
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