End To End Testing

I am having difficulties setting upp an environment that executes end-to-end tests. This is probably because i dont get the whole concept yet, but this is what i want to achive:

Have the jenkins server, that is installed on the droplet, run my selenium-protractor-jasmine end-to-end tests when there is new stuff in the repo. I have the hook and all set up, and jenkins detects new content, but how do i get the tests to run…? I need to be able to spawn a browser, so i installed xorg, if i ssh -X to the droplet i can start a browser, but how do i get the tests (or perhaps Jenkins) to do that?

Is it possible for a service so spawn a browser within the droplet itself, since it cannot ssh -X, if so how?

Or, do i have to place jenkins in another droplet, and ssh -X jenkins into the droplet where the tests are, and spawn a browser in that way?

Any help would be greatly appreciated!

Cheers!