I can suggest two options.
1: You can save an RDP connection (see picture below) and just run the new .rdp file from WshShell. After you create the .rdp file, you will have to log into it the first time, enter your credentials, and check the "Remember My Credentials" option.

2: You could use the SendKeys method. It is ugly but works. The downside is the password is left in the code, so you may want to look into encryption if you go this route. You may also need to tune a wait (sleep) for waiting for the popup to come up.
WScript.Sleep 5000 'Sleeps for 5 seconds
SendKeys “{TAB}”, 1 'Focus to the computer name
SendKeys "ServerName", 1
SendKeys "{TAB}", 1 'Focus to the user name
SendKeys "Password", 1
SendKeys "{ENTER}", 1 'Connect