Using a Desktop & Mobile Theme together

I’m wondering if there is a way to run two different themes pulling the same information. So basically my issue is I have a woocommerce store which I want to have a mobile version of but I’d rather use an app/theme like AppPresser to have the mobile version instead of trying to make a complete mobile site.

I don’t mind having a m.sitename.com or a /mobile/ extension but I want all the data and pricing to update from the same database.

Is this possible?

Thanks!

https://www.ads-software.com/plugins/woocommerce/