Any particular reason for this structure, AAMOI...?

I guess it would depend on the backend RDBMS. If it's SQL Server, I would go
for the factory pattern described in Microsoft's DAAB:
http://www.dotnetjunkies.com/Article/29EF3A4F-A0C2-4BB2-A215-8F87F100A9F9.dcik

//SqlDataSource1.ConnectionString = Session("dbconn")//

Ahhh......

Just stored the connection string NAME.... as the most recent picked item

{
   ConnectionStringSettingsCollection connectionStrings =
ConfigurationManager.ConnectionStrings;

   ConnectionStringSettings connection;
   foreach ( connection in connectionStrings) {

       string connectionStringName = connection.Name;
       string connectionString = connection.ConnectionString;
       string providerName = connection.ProviderName;

       Debug.Print(connectionStringName);
   }

   this.GridView1.DataSource = connectionStrings;
   this.GridView1.DataBind();
}

Get rid of those stupid "auto generated adapters" (FillTable) things when
you create your Strong DataSet.
Those things are the devil.

You can get something like the EnterpriseLibrary.Data to help if you want.
Either way, write a real DAL object ... which will populate your strong
dataset... and pull the connection string info from the config file, using
the simple NAME passed into your DAL object.

That auto generated stuff is for the birds, esp when you want to pick the
database dynamically.

class ZebraData
{
   public  static ZebraStrongDS GetAllZebras( string connectionStringName ,
string zebraColor )
{
   //pull the connection string from the config file with the objects above
   //
      ZebraStrongDS  returnDS = new ZebraStrongDS ();

   // i threw in zebraColor as a param...
   //call LoadDataSet method here, to populate the returnDS with
resultset(s) from a stored procedure or something

}

}

You can check my blog, I have several NLayered (and now 1 NTiered example)
there:
http://sholliday.spaces.live.com/Blog/