Exploring Smart Home Integration with Vera 3

I’ve been using a Vera 3 for a few years now and have upgraded it to ui7. I’d like to make an android app to allow control from wall mounted tablets in my house. I see on local networks how you can simply make http requests to interface and do everything I want. However, I can’t figure what is necessary to remotely accomplish the same thing. After a few hours of searching I can’t find anything, so I must be using bad keywords. What should I be looking for? It’d be nice to be able to use the same app on my android phone.