Setting up HTTPS configuration is easy ...

To build additional security on special pages on a website (e.g. a user form), the module Secure Pages has proved its worth. With it, you simply configure a domain within Drupal to be used for the secure connection, (provided that the server is configured correctly). With additional settings, you can specify several pages to be secured.

... and a mobile domain too, ...

To provide your page with a special theme for mobile devices, the module Mobile Tools is a good solution. You simply enter your mobile domain in the configuration and mobile devices are redirected to that page, with the theme switched to the selected one.

... but they don't want to work together!