It sounds like what you want to do can be accomplished if you build a Shopify App that uses the App Proxy functionality. With an App Proxy enabled for your Shopify app you can route requests from your shop’s domain to any url of the app’s choosing. For example you can route from https://your-shop.myshopifycom/apps/test-app could become a direct link to https://your-own-php-website.com. Now when customers go to your Shopify store and visit that link on your store, they will see all the content from https://your-own-php-website.com without leaving your store.
There are unfortunately no PHP examples to share, but there are plenty of helpful documents: