Hey,
I was having the same issue and got here looking for a solution. While what you are looking for would be a feature request, I'd like to share how I solved half of the issue, more specifically the ctrl+arrows
part.
- In macOS System Preferences, navigate to Keyboard > Shortcuts tab.
- Uncheck the boxes for Mission control, Application windows, Move left a space and Move right a space. Alternatively, assign other keyboard shortcuts for those actions if you like using them.
Unfortunately, there is no workaround for disabling the four-finger swipe when Remote Desktop is active, apart from disabling it entirely in System Preferences > Trackpad, which doesn't seem to be what you are looking for. As I said, that would be understood as a feature request, and I'm not even sure that it is doable on the API level.