to redirect http and https from remote apps or remote desktop sessions to your local internet browser use Remote Executer For Terminal Server  by mqtechnologies.com.

Http & Https redirect (client must be installed on each PC + Remote Desktop Server)

For full notes see  http://www.mqtechnologies.com/en/TSRemoteExec.aspx –
Registry edit on each Remote Desktop Server, as follows:

1. Change Default Value at HKEY_CLASS_ROOT\HTTP\Shell\Open\command

TSRemoteExec %1 /DEFAULT:”C:\Program Files (x86)\Internet Explorer\iexplore.exe”

2. Rename HKEY_CLASS_ROOT\HTTP\Shell\Open\ddeexec and rename it to ddeexec _bak 

 For 64bit client machines see

http://www.davidmoore.info/2009/12/02/running-32-bit-remote-desktop-connection-on-windows-64-bit/