Let me take a shot at this.
First, if I remember corectly something I once read. What your attempting to do is more or less a security risk for severs. Let me explain. In PHP all the php code is handled server side before it goes to your browser. What you are wanting your host to do is include/process a file from a differnt server. Now admittedly there is probably no real risk in doing this for the site you wish to include from but giving that ability to a half way intellegent hack would be a big security risk for your host.
Next, there is the issue of the server having to find a "something.com" domain name. Your ISP's severs can do that because they are set up to know were to look up the IP address for that domain name. But a web hosting server doesn't usually have the ability to look up IP addresses for domain names unless they are stored on there server(s). So if you could include a file from a differnt server you would have to have the other servers IP address and the folder sub-folder structure to get to the file(s).
Now, I am sure what you are wanting to do is possible, but you will need a program (kind of like what search engines use) that can retrieve the already proccesed html from their site and then have it look for each link in that html and replace it so as to use the program, again, to retrieve the new links and so forth and so on.
I hope I didn't throw to much cold water on your fire but there are some obsticals to over come. And it's going to take more than a basic knowledge of PHP to over come.
Something you could look into also, is the site you are wanting to get the pages from, you may want to see if they have an API setup you could access (usually a very large site), or if not a RSS feed that you could use. Also if what you are going to do will generate traffic that will make them money (via adds or services/products sold) they may be willing to work with you on a solution.