CNAME Record domain forwarding breaks emails due to MX Records mis-match

CNAME Record caused my emails to fail.

I hosted 2 emails at RackSpace for my domain, and verified they worked fine. This required me to update the MX records where I host my domain.
name1@domain1.com
name2@domain1.com


Fine.

Then, before I could create a website, I was allowed by my partner to point my domain at his website.

The redirect worked once I created a CNAME record.
domain1.com brings up the site at domain2.com

But the emails stopped working.

The error is "553 Relaying disallowed"

I called RackSpace and they said it's because the MX records at the domain2.com, where domain1.com points at, are pointing to Zoho (a major email provider).

So, my question is...

If I move my two emails from RackSpace to Zoho, can I have a solution where

1) domain forwarding is working (domain1.com brings up the site at domain2.com)
2) emails work as well (both (domain1.com emails work again)

?

Thanks.

Or, is there another way to configure this?

Thanks