The problem is very odd indeed. If you could have tested this from two different internet connections (ie, so you get two different IPs), it'd probably work, but I can't say for certain, of course.
I suspect, though, that the problem is NAT related. NAT = Network Address Translation. It wouldn't be the first time NAT is making trouble for people.
If NAT really is the problem, this can be for several reasons. It could be that Funcom is pulling some stunt to avoid gold-spammers. I think that would be surprising, but it is a possibility. That you can log on Em logs in first, and then you, however, makes that rather unlikely.
NAT in general is the cause of a lot of problems. It _could_ be your router not handling it properly. Your router will have to keep track of Em's and your connections at the same time, and sending the traffic to the right computer. Usually, this shouldn't be a problem, but sometimes, it still is.
But you've both been logged in at the same time, right? I doubt you'd get past the account creation, though I suppose it's theoretically possible.
But what happens if you log in with your account from Em's computer, and Em's from your computer? ie, switch from the way you normally do it? That too might help give an indication on whether this is caused by your PCs, at least.