I'm sorry you are having issues with your device.
I think that we can try something called "Protocol Binding" which will make sure that the devices use a single internet connection when trying to connect to secure sites.
Here is a link that shows how to configure Load Balance and several other features: http://sbkb.cisco.com/CiscoSB/ukp.aspx?vw=1&docid=d297d2890f084031a5e906f24727104c_Set_Up_Dual_WAN_Connections_.xml&pid=2&respid=0&snid=4&dispid=0&cpage=search
Go to the part called "Managed Protocol Binding" and create two rules to bind ports 443 and 8443 to the WAN that you would like to use to connect to secure sites.
On the protocol binding page, for the source IP, use the range you have in your LAN, for example, you can use, 192.168.1.1 to 192.168.1.254, as for the destination you ill need to use 0.0.0.0 for start and finish. When you use 0.0.0.0 you are indicating anywhere on the internet.
I hope this helps.