The azurewebsites.net domain is provided as a simple free dns & ssl solution, it doesn't support this scenario.
I'd suggest;
- Buy a domain, and leverage custom domains to facilitate the configuration
- Leverage 2 regular azurewebsites.net domains in the two different apps
- Use one Web App, and create virtual directories for each app.
examplepeter.azurewebsites.net/app1 and examplepeter.azurewebsites.net/app2