well, ideally you would set up the web browser connection as the VPN for the RDP session. In this scenario, simply double clicking on the RDP connection would open the web session.
In the VPN tab of the RDP session, select an "active" value for the Open setting (connect if unable to ping is our favorite)
Then select "existing session" for Type
Then select your web browser session in the session drop down
In the VPN tab of the RDP session, select an "active" value for the Open setting (connect if unable to ping is our favorite)
Then select "existing session" for Type
Then select your web browser session in the session drop down