Which Remote Desktop works with Control Keys?
I would recommend RealVNC VNC Viewer.

It allows the capability to use all the keys on a real keyboard (command, control, option, etc.), even the function keys. Almost any remote deskop application out there uses VNC to handle the screen sharing. VNC Viewer works just fine with Apple Remote Desktop and Bonjour, Terminal, Xterm, and iTerm2 — just open port 5900.

*There's a free version, and a full version (normally $10 for iOS), although the full version is free at this very moment, so grab it while you can.