Hi John,
You can run an exe by making your form Full Trust and writing code that calls the cmd line but I don't recommend it because it complicates your form.
Better solution is to use a server-side trigger (perhaps a workflow) that kicks off when the form is submitted. Do you have SharePoint 2007 with workflow? It will require a custom workflow that is installed on the server.
I'm guessing you need to do this synchronously. If not, you could just set up the VB program to run every hour and check for new records to process.
Another random idea is to send these XMLs to an email account and add the custom command as part of the Exchange server.
Or, you could just have a link in your form that calls an ASPX page (on SharePoint) that runs the script and processes the XML - that might be the simplest.
Hopefully, one of these ideas will provide a spark to get your engines blazing... if not, sorry to be lame!
Cheers,