There are many foreigners here. It's just that most of us seem to write better English than many Americans...
But as for REMOTE_ADDR, that's probably as close as you'll get. Here's why:
Let's say your picture of what's happening is like this:
User (100.100.100.100)
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Domain B (123.123.123.123)
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Domain A (200.200.200.200)
Now Domain A's value for $REMOTE_ADDR will be 123.123.123.123 - that is, Domain B's IP. Domain A has no idea what the Users's IP is. Domain B knows, but it hasn't told Domain A.
Now if Domain B operates through a proxy server, the situation becomes
User (100.100.100.100)
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Domain B (123.123.123.123)
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Proxy (155.155.155.155)
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Domain A (200.200.200.200)
Now Domain A's $REMOTE_ADDR will read 155.155.155.155 - the Proxy's IP. Domain A has no idea what Domain B's IP is, and the Proxy isn't going to tell.
In the situation you describe, it sounds like your hosting firm has set up a proxy, and any requests from its hosted domains pass through it.
You may want to check with your hosting company to see if the IP you're getting really is theirs (I'm willing to bet it's one of their proxy servers).
I was going to say that it would be possible for them to reconfigure the hosting server to bypass the proxy, but then I realised that it would be pointless - you'd need the IPs for Domain A and/or B, and if you had those you wouldn't need the script! :-)
So the short answer is: you'll only be able to get the IP address of the last proxy in the chain between Domain B and Domain A. it's the proxy's job to make sure you can't see any further back than that.