We have the following set up:
When we map a domain to one of the stores, it seems to work in that you can access the store on the mappped domain. The issue is that you cans till access the store on the old unmapped domain.
So, if we visit 'their_name.com' we get to the store fine. If we visit 'oursite.com/their_name' we still get to their site and the url is not changed to 'thier_name.com'
The other issue also being that if you are on the store on 'oursite.com/their_name' and you try and add something to the basket, you get an errod.
I'm raising it against Domain Mapping as I suspect it's around this but may be wrong.
Any ideas? Is this a configuration issue? We have had to remove domain mapping for now as the store owner wasn't happy so I can't let you take a look at the site itself.