How can I stream my desktop to another device so I have complete control over it?
I'm working from home on an iMac, accessing two iMacs at our office through a VPN, and I'm using the "Screen Sharing" app that comes with Macs by default (at least up to Mojave) and is located in /System/Library/CoreServices/Applications (again in Mojave, I think they have moved it around depending on the version). I have my home computer with five Spaces, one work computer with four Spaces and a second work computer with just one Space.

It works pretty well, but any gestures that work with Mission Control or switch between applications are caught by the machine you are physically working on.

As a workaround, I've been putting the Mission Control application on each remote computer's dock, so I can bring it up manually and switch between Spaces, etc. on the remote computers. The keyboard ⌘ Command ⇨Tab does seem to work in that it switches between applications on the remote computer, so that might be a workaround for swiping between apps.