So you have Cisco AnyConnect Secure Mobility Client and IBM AT&T Global Network Client VPN and you need to use both? Well have no fear, you can use both. In your windows, right click the Cisco AnyConnect Secure Mobility Client, then “Open AnyConnect”, from there click on the gear on the left side in the GUI to open up settings. In the Settings dialog menu, go to Preferences tab and check “Allow local (LAN) access when using VPN (if configured). This close the dialogue, disconnect from both VPN and reconnect to Cisco AnyConnect then IBM VPN and you should be able to use both.
Hope that helps,