Question: I have a MacBook Pro with a touchpad, and the only way I can figure out how to use the right click in my remote desktop session is by plugging in a mouse. 

`Ctrl`-click (what I usually use for right click), doesn't work, as `ctrl` is used in Windows for other things. Is there an alternative?

Answer: 
This is kind of embarrassing, but the real problem was I didn't know how to right click with a touchpad on the macbook (it was still less than a month old). Update: You can do this by clicking or tapping with both fingers at the same time.
I found that you can simulate the RIGHT-CLICK as follows;

use the arrow to position where you wish to right-click
then use the keyboard icon and select SHIFT and F10

When you tap the keyboard pad to disappear you hopefully will have the right-click menu you want.