There are a few too many variables and bits of information missing to give you an answer straight off the bat, so I'll dig a bit deeper.
So the SIP soft phone registers to an MBG server? uca.domain.com should resolve to the public IP address of the MBG server.
Configuring AWC (or MCA as it is now known as) is best done by your VAR/Mitel Partner. It isn't an easy task, and beyond what can be detailed on here, plus it should be installed by a trained Mitel Tech, as otherwise you wont get any support from Mitel on any issues you may have. There is a difference between configuring MCA for internal use, and then breaking it out so that it can be used externally as well, as that then requires the MBG server with the Remote Proxy Services on it.