How do I open a remote desktop session on a secondary monitor?

I don't know if this helps, but in my experience, Windows tends to remember the monitor on which the app is maximized. Try opening RD on the second monitor, maximize it, close it, and see if it opens on the second monitor when you open it again.

Here's complete guide from Microsoft on how to do it: http://social.technet.microsoft.com/wiki/contents/articles/665.how-to-set-the-monitor-for-a-remote-desktop-session-in-a-multi-monitor-setup.aspx

Try this:

winposstr:s:0,1,2142,150,2942,750

It worked for me

Open the RDP file in a text editor, find the

winposstr:s:0,1,xpos,ypos,width,height

Change the xpos and ypos in the RDP file and save it.

You can then have the window open consistently where you want it.