I regularly redeploy apps to shinyapps.io from different machines. Because the app was never deployed from the new machine, my IDE won't show any options to update it. I have to connect to my shinyapps.io account, and then deploy the app.
If you redeploy the app to shinyapps.io with the same name as an existing deployed app, the dialog will ask you if you want to overwrite the application. ("You've already published an application named {your-shiny-app-name} to shinyapps.io... Do you want to replace the existing application with this content?") In the IDE, in the publish dialog, the name of your app is the "Title" field.
I think these steps should help you update your shinyapps.io account, but let me know if it doesn't.