So it think the real question here is
Can anyone confirm what pass-through authentication details are sent to the trusting domain ie. DOMAIN\username and password, or just username and password? If just username and password, is there any way to change this
So... if you have at a minimum a One-Way Transitive Trust see http://technet.microsoft.com/en-us/library/cc736874(WS.10).aspx for details on Trusts... then you are good to go. By default it will send Domain\Username accross since the domains are in-fact different. and if you have your Zones configures which it seems you have everything right.
The only thing that i know of that will cause you to experience what you are dealing with is IF you are trying to open a document in a Library on the inside, cause Office will want to authenticate you agian and that is different than the NTLM challange.
To test that your Trust is working may i suggest a test.
See if you can find the user in the People Picker?