need help with exim setup

[Paul E Condon <pecondon@peakpeak.com>]

I have ppp connection to my ISP, peakpeak.com.  I have a LAN for my
wife's iMac and my two Debian machines. All internet traffic goes thru
the single ppp connection. I have set up exim using choise 2 in the
exim config. I use pecondon@peakpeak.com and my wife uses
cfcondon@peakpeak.com.  Email to and from the internet works for both
my wife and I, but ...  

1. I can't send email to my wife, and 
2. I can't send email to ISP support services, 
for which the address is support@peakpeak.com.  

I think that these two problems are the result of improper
configuration of exim. Exim seems to be attempting to deliver both
kinds of email locally rather than sending them out to the smtp
service at the ISP, and, of course, it can't deliver because neither
address is known locally. For my wife, I wouldn't mind having local
delivery, but for the ISP's support, I definitely need to send the
mail off site.

Am I right about this being an exim config problem? And, 
what should I change to fix it?

TIA

PS Why email my wife? We do talk to each other, but stuff about
software updates for the iMac come to me, and forwarding the email to
her would be a reliable way to get hot-links onto the iMac.

-- 
Paul E Condon           
pecondon@peakpeak.com