Our internet connection is slow so that rules out using wifi tethering.
Did you mean WiFi Direct connection?
With WiFi Direct, it should be faster than the regular wifi connection since it will not go through the router anymore.
spacedesk connection also does not require internet connection.
What is your primary machine operating system? Windows 8.1 or 10?
For analysis, could you please run dxdiag.exe on your primary machine, click "Save All Information" then save the output file (dxdiag.txt) and attach it on your next reply.