I was running into this same issue myself. I'm running 10.1 SP1 and was able to successfully implement this workflow using an existing CA cert. The setup was extremely sensitive and would only work for me when done in the following sequence.
1)Install CA cert. on IIS
2)Enable https and http in AGS Admin.
3)Restart Server (this is key)
4)Log back into AGS Admin. Choose and save settings *again for the "self signed" cert. (the default one)
5)Run web adapter with the "https://xxxxx:6443/arcgis/admin" for admin dir.
These items in this specific order were the only way I successfully implemented using SSL with an existing CA certificate while maintaining http & https access. It was a lot of trial and error to make this work. Hope this helps some of you out there.