Don’t capitalize grandmother unless it’s being used as a proper name: “This is my grandmother; I call her Grandmother.”
Add a comma after router (long introductory phrase).
The second sentence needs a slight adjustment so it doesn’t imply that the unplugging, the yelling, and the disappearing all happen at the same time. Adding then before promptly disappears will make the sequence of events clear.
Replace the ellipsis with a period, because an abrupt disappearance of a grandmother isn’t the sort of situation you’d describe with a trailing-off at the end.
Your grandmother asks you to fix the internet. As you pull out the plug for the router, she yells, “Not that one!” and then promptly disappears.