You could potentially use tags$iframe for this:
It wouldn't be a single R process solution however.
# app1
ui = fluidPage(h1("inner"))
server = function(input,output){}
shinyApp(ui,server,options = list(port = 8000))
# app 2
ui = fluidPage(h1("outer"),
tags$iframe(src = "http://127.0.0.1:8000"))
server = function(input,output){ }
shinyApp(ui,server)