I wish there was a way to use a mouse click to switch spaces

Note: this is about using a 2014 Mac Mini running Mojave through an RDP (Screenshare) session on a 2018 Mac Mini running Catalina. The issue is the same in both -- it's the undocumented nature of how Apple manages Spaces, so nobody can write apps that do anything other than Apple without using undocumented API calls. Spaces exist, but there are no documented API calls to work with them. So I'm asking about something that technically may be just a mirage...

I've been using a 2014 Mac Mini with 10 Spaces. Love how they work! I got a new 2018 Mac Mini and cloned the old one, so it's set up the same.

To avoid needing duplicate peripherals, I set up Space #10 in the new one where I open an RDP window (Screenshare) to the older machine. Works like a charm! I just hit <ctrl>-0 to access the other machine and viola! It's there!

Except ... none of the alt-keys get sent to the RDP window! So I can't use <ctrl>-3 to switch to Space #3 inside of the RDP window. It goes to Space #3 on my main machine. I can't use mouse gestures either, or the hot-corners. So switching spaces in the older machine in the RDP window is problematic, to say the least.

Curiously, I use VirtualBox a lot, and when it's running, it DOES capture ALL of the alt-key combos. So to switch to Space #3 on my host machine, I need to move the mouse outside of the VM window and then click <ctrl>-3.

I don't know why Apple's RDP/Screenshare app won't accept alt-key combinations, but until it does, I need some means of switching Spaces using a mouse-click.

I found a small app in the App Store named Virtual Desktops, but it's read-only. It would be perfect if I could click on one of the icons to switch a desktop when it's set to display one for each desktop.