If you have a standalone VPN client program (i.e. Cisco AnyConnect), use Google to find commandline options for that product to see if you can connect with a single command. For example: AnyConnect, the generic Cisco client, and the Windows VPN client all support this. This might require you to store your password in plaintext in a batch file or script, however.
Once you have that info, write a batch file which invokes the VPN client, probably sleeps a few seconds to make sure the VPN link is good, and then calls the remote desktop client from the command line.
If you wanted to be really fancy, instead of a sleep to verify connectivity, you could have a ping to some resource that's only accessible over the VPN, and have the script return an error if that ping doesn't succeed.
Take your batch file, put it (or a shortcut) on your Desktop or wherever, and then you have a one-click "connect to the VPN and then open Remote Desktop" app.
If, on the other hand, if your VPN client is such that you can't connect via the command line, I'd look into AutoIT or other mouse/keyboard macro scripting languages to see if you can automate VPN connection.