Welcome to Shopify Community. My name is Olivia and I work here.
It sounds like you are running into some issues with the mobile version of your site. I wrote this great tutorial on narrowing down issues on your site, that I encourage you to check out here.
By following the troubleshooting steps in that tutorial, you will be able to further narrow down if there is a theme code issue, or if perhaps an app is interfering with the button.
I trust that will help guide you to a solution, but if you have further questions for our team don't hesitate to reply here.