Using discord video externally

Theoretically is it possible to use Discords video chat API (not even sure if that's the right terminology) on different platforms? For example, I'm currently building a website for teaching Korean students various subjects in English by linking students with compatible teachers (similar to Italki but with younger students in mind), and having the ability to have a server, the ability to video chat and post homework and assignments in one location is the goal. Discord is amazing for this but in a location that's not super convenient. If they sign up with our platform we wouldn't want our users to have two apps open at the same time. Instead, they could just use their discord account through our platform and video chat from our platform. 

My only question is, is this theoretically possible (having discords services "tunneled through" to our website), and has it been done before? Upon searching through the various sites, I have found nothing which relates to what I'm searching for. 

Thanks in advance.