If you don’t mind getting your hands dirty with code you could combine both themes into the same folder. IE: wp-content/themes/yourtheme/secondtheme
Then add the code in the header.php for your primary theme to check if its a mobile site and send the user to wp-content/themes/yourtheme/secondtheme/index.php
Probably a pretty big nightmare.
The proper way of doing this is to code the mobile theme into your theme. These type of themes are called “responsive” meaning they conform to what ever device is viewing them.