Remote desktop with multiple monitors

I have a laptop to which I have connected a larger LG monitor. My aim is to log into the desktop, do a remote desktop on the large monitor to which I log into work. I get this to work sometimes almost randomly. Here is the thing.

I want to have the full screen so I don't have to scroll the remote desktop up and down. So I check "full screen" in the options. When I run the remote desk top it does in fact use the full screen but it is on my lap top monitor not the LG. I exit and move the remote desktop icon to the large (lg) monitor and run it again, but it goes back to the laptop monitor. I can't move it when it is enlarged or when I click the "-". If I click the little icon (not sure how to describe it but it is one square on top of another but slightly shifted) it makes the window smaller. Then I can drag it to the other monitor and maximize it, but it then has the scrollbaer and is not using the full screen.

Somehow I got this to work before, but my drive went and they installed a new drive so I had to start over again.

Can anyone tell me how to get the remote desktop to open in the Large (lg, monitor 2) monitor using full screen?

(Please note I realize once I remote desktop into work the windows open in remote desktop won't be able to be moved to the laptop screen but that is OK).

there may be other ways to do this since you said you have it working before, but the program Ultramon allows you to set certain apps automatically in maximize mode on different monitors.

Thanks. Not sure our sys admins will allow us to install that, thought.