Restricted Remote Access

I belong to a marketing company with clients who have databases residing on their local computers. We would like to write a program, say written in visualbasic, which would reside on the client's computer, and retrieve and display very specific, limited information from their database. We need to be able to access this program from our computer. And our clients need to know that access to run this program is the only access that we have to their system.

How would this be implemented? It has been suggested to us that pcAnywhere or GoToMyPc could easily accomplish this. Is this true? How does it work? Does anyone have experience with a comparable situation? Are there alternative solutions? How could we make the client feel secure and comfortable that we are not "breaking into" their computer system, but rather only accessing this one program that we need?

Ideas for solutions would be welcome. My background is html/javascript/Server Side code, and my knowledge of networking is not extensive, so details would be helpful, as would suggestions for forums which might be more suitable for this question. Thank you.

PC Anywhere and things like that would give full control over the computer, which your clients would probably not want.
What I suggest is as follows :

Write a small application that connects to the database in much the same way that their own users would.
The application communicates back to your own central applications there to provide information etc.

There are 2 ways in which this could be done :

1)
Your application is listening on a particular TCP port.
Tell the client to set a static IP address on the computer running the application.
Have them enable port forwarding on their firewall/router, and have some particular port number forwarded through to the listen port on that computer.
You use an application inside your own network to communicate with the application at the client.
You would implement a custom communications/handshake protocol to exchange information.

2)
You have a central server/application in your company.
The client application connects through to the server application.
Information can then be sent or requested over this connection.
You would enable port forwarding in much the same way as above.
The advantage here is that you don't have to ask the customer to configure their firewall to allow inbound connections onto their LAN.