someone else serving my mx record

[Herman Mudget]

I have a co-located Server, which I am setting up to relay mail.  I
already have    dns  services via my ISP. They have added an MX record for
foo.com so I can ping mail.foo.com. On the server, I also setup the DNS
servers to be my ISP's. 

Problem is, sendmail can't qualify it's own domain name.  This leads me to
believe that I need to run its own dns services on the box for sendmail to
run.  A friend said that what I need to do, is locally setup a hierarchal
lookup so sendmail can qualify its own domain name.  Essentially, I want
to run tertiary dns services on my server, since my ISP already has my
records configured.  If at all possible (read if it doesn't make a byte of
difference) I'd rather not change my network solutions record. I would
like someone to tell me if what I want to do can be done, before I find
out the hard way.

Also, could someone point me to the difference between running named and bind?

this is all much appreciated.

mudget