For what it's worth, all of laravel, except the frontend parts, is plain PHP. ;)
It would behoove you to learn the framework properly, rather than just trying to hack things in in a messy way.
That said. This would probably be a good candidate for implementing as an event, probably even a queued event if it's going to happen a lot. As @rsands mentioned, api credentials should be pulled out to the .env file, ideally.
If you're using laravel 5.3, best place to do this, probably, would be as a custom notifications channel. SMS is already available with notifications via nexmo, but if you want to use txtlocal.com, you'll probably need a custom channel.