You will need to understand how the code is built and change it a bit. It is quite simple.
Replace rdcConnector1 with rdcConnectorA and rdcConnectorB.
Each one of them will point to a different database (you will need to take care of loading the correct configuration file).
Now in RDCHandler add this to Class_Globals
private connector as RDCConnector
private connectors As Map = CreateMap("a": Main.rdcConnectorA, "b": Main.rdcConnectorB)
You will need to add an additional parameter to the query (together with the method parameter). Lets call it database.
Dim method As String = req.GetParameter("method")
connector = connectors.Get(req.GetParameter("database"))
The last step is to change the references to Main.rdcConnector1 with connector.