make website run through a different server

I have a hosted CMS on a VPS running apache 2.2. I have a client in China who says the search engine Baidu ignores their website.

I wonder if there is a way to have a Chinese domain (website.cn) on a server in China, but operating as though it were an "add-on" domain to the CMS. This would only be for the public facing website. To administrate the CMS, the staff in China would still access the server in the U.S. as they always have.

The result would be that users in China could type: http://ift.tt/2dGJzcW

and the result would be the same as though they had typed

http://ift.tt/2dX6XOq