We own a print-on-demand serivce allowing people to create and sell personal care and pet care products. How do we go about developing an app so that customers can easily integrate to their website and sell their products?
For reference, exactly like printful but for cosmetics instead.
Hi there 
I would recommend starting out with the developer documentation about building Shopify Apps. Building a Shopify App is highly technical and will require the expertise of a software developer. Here is a tutorial that guides you through building an example Shopify App.
Your Shopify App would use the Shopify API to create and manage products that the merchant is selling.
Once the App has been built you will submit it for review in the Shopify App store.