You're going to have to provide more detail on how the SIP trunking is delivered.
There are basically 3 ways ITSP's provide SIP trunking.
1. Via a secured connection like MPLS. If you do it that way, you will have a separate router and some kind of network interface device like an Adtran box. This is the most secure and expensive way for SIP trunks to be delivered.
2. Via a separate standalone DSL type connection with dedicated bandwidth. Generally this connection is unsecured and requires you to use a username and password to register to the SIP provider.
3. Via your existing internet connection. This is the cheapest and most unsecure method of delivery. You just need your account credentials to register your system to the ITSP.
Given that your supplier has supplied you with a private IP address, my guess is that they are using method 1. If that's the case, you will need to know what their host ip address is (or resolvable host name). You will need to enter this info in the peer details of the trunk configuration. The IP address you need is the one for the sbc at their end, not the private one. To test it all, you might want to change the ip address of the UCx to be on the same subnet as the address they gave you (ie 10.116.0.125)
Here's a sample configuration you can try to see if you can get connected:
type=peer
sendrpid=yes
rfc2833compensate=yes
relaxdtmf=yes
progressinband=no
insecure=port,invite
host=the ip address they gave you or their host name
dtmfmode=rfc2833
disallow=all
context=from-pstn
allow=ulaw
Incomind Details:
type=peer
trustrpid=yes
sendrpid=yes
rfc2833compensate=yes
relaxdtmf=yes
progressinband=no
insecure=port,invite
host=the ip address they gave you or their host name
dtmfmode=rfc2833
disallow=all
context=from-pstn
allow=ulaw
Good Luck and let us know how you make out.