Now I am not hosting with the same provider, so I could be wrong, but it looks like your second connection is correct.
Your first needs to be written like the second.
I looked at domainsrightnow and it looks like it is a lot like GoDaddy, I am assuming that you set up with the deluxe plan, so you would get 2 MsSql databases.
And when I did it, I created two databases, on godaddy it created all the standard aspmember tables automatically.
So the members database needed no manipulation, and the Ads Database I had to delete the auto created tables, views, and stored procedures.
Then it had a tool called query analizer, basically it runs Sql scripts.
I used a database program to convert my altered database to Sql and ran the scripts.
If you made no modifications to your database then you can use the included .sql files in your App_Data folder.
I can go into more detail if you need it.
But I think the main problem you are having is that your connection string is telling the application to run the Ads database locally.
So start with writing your connection strings in the same format as the second, but pointing to the two databases,
Ads first then the members one second.
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