Once again, you can't just drop an ASP.NET application into your SharePoint server. If your company and SharePoint dept feels this is best then they all need to gain a better understanding of SharePoint. A sandbox solution has nothing to do with this context unless you are providing a SharePoint solution and wouldn't make much sense anyway as your solution would need to make use application page most likely. A PageViewer[^] webpart would provide the functionality to link the external pages. However, any security tokens, if necessary, are not sent to the other site by default unless you have SSO configured.
Failure is not an option; it's the default selection.