Not a fan of remote play controls, but still want the second screen function?
Well I got a solution for you! After messing with my Vita, I figured out how to use my DS4 while using my Vita as the screen.

Step 1 - Sign into your PS4 with a secondary account (anyone that isn't linked to your Vita).
Step 2 - Take your Vita and connect with remote play.
Step 3 - Pick up your DS4 and start gaming!

But what if someone else wants to use your Vita as a screen, but doesn't want to play on your account? Here's how you do that!

Step 1 - Connect via remote play and sign into your primary account (the one linked to the Vita).
Step 2 - Take your DS4 and sign into any secondary account.
Step 3 - Start gaming!