I understand exactly the nature of your problem, but unfortunately, not how to solve it!
My own setup is very similar to yours, except I can access my installation from both the serving machine and via the internet. I am not aware of anything special I did to achieve this. When I got my new fixed ip address, I just substituted that for the private (192.x.x.x) ip address I had been using to view my site locally.
What you need is advice on masquerading. I've seen your issue crop up time and time again on these forums, and masquerading seems to be the answer.
Unfortunately, I don't understand it sufficiently well to give you a more thorough explanation, but I suspect that others (RLE, KW and MK to mention a few) could fill you in with more details. I don't have this problem with my own installation, but in work, I do have this issue - I cannot access from within work, but can from outside. If I change configuration to allow local access, then web access is lost.
I'm sure one of the others will pick up on this discussion, and in the meantime, you should check this link to the FAQ and the subsequent link to masquerading on that page.
Sorry I can't be of more help, but I just don't understand enough about masquerading to fill you in.