Is it possible to easily control an Arduino project remotely over the internet?

Hey everyone,

I'm still pretty new to the Arduino world and I currently have an Arduino Uno. A project I'm trying to do is a remote control laser pointer turret that also dispenses treats for someone so they can remotely interact with their cats at home while they are at college. Also, the live video system would be a separate system from the Arduino.

Making the physical product shouldn't be a problem but how can I remotely control the motors assuming it's plugged into a PC? Also, how would the "control" system on the user's end be handled? Is there a way to make, for example, the laser pointer move up and down using the arrow keys?

One idea I have right now is finding a way to send serial commands through USB to the Arduino and using a remote desktop to access the computer the Arduino is plugged into.

I would use MQTT over the internet.