[exim] Will using a smarthost give me problems with checks o…

I use exim 4.69 on ubuntu Hardy Heron. The server is not the mailserver for
the main domain, but handles mail for a small, separate, domain. Recently
the admins of the main mailservers have changed their config so that the
main incoming mx servers won't receive mail from a machine on the local
network - only from a remote network. Thus if my server sends mail to the
main mailserver, it fails.



I can use the main outgoing smtp server as a smarthost, then it all works.
However am I then setting myself up for rejections from other, remote MX
servers, because mail from my domain will appear to come from the separate,
main domain (as a result of going through the smarthost)? Or will it be
fine?



Is there a different workaround that would enable me to send directly for
all domains except this one, which would use the smarthost?



Thanks for any advice,



Rich