I have added a CNAME from order.checkoutchiangmai.com to restaurant1.acemsweb.com. The result I have is a "Apache is functioning normally" message with a white background when I open order.checkoutchiangmai.com. I am unsure why the restaurant1. domain does not show, as when I check the dig command in terminal it appears correct. Thank you.
order.checkoutchiangmai.com. 3600 IN CNAME restaurant1.acemsweb.com.
restaurant1.acemsweb.com. 3600 IN A 27.254.86.7
Edit: Added Apache detail
You can try using ServerAlias in your restaurant1.acemsweb.com vhost configuration.
ServerName restaurant1.acemsweb.com
ServerAlias order.checkoutchiangmai.com