Receiving external and sending email external

Great day all,
I have this company that is called Care.com that I am contracting my IT service to. I have set up an in house exchange 2010 box. Previously the gentle man before me had their email outsourced to networksulotion.com on server smtp300.server.net.
This company at one time was using hover.com to host there domain  care.com. I have transferred there domain from hover to godaddy. That went well. By doing so that gave me access to theire dns so I can make changes to the dns Mx record so mail would start going to my server ( I hope that was right). Under my godaddy  I have other domains. Therefore, I decided to use one of my other domain dns as a test to make sure it would work. So under the domain back.org I set up the dns MX recorded as xx-exchange2010.care.com to point to the in house exchange with the same MX record.

The naming convention root for sending mail for his (smtp300.server.net) is @care.com and mine (xx-exchange210.com) is @care as well ,is that a problem. His is receive the client mail now and mine is not. Do he need turn off his service  in order for me to get mail on my server which is in house.

Is it possible to get email for this company on two different exchange box?


 I hope all this made since