Okay. So I saw a post on Reddit from a guy who showed off some different weapons and animations he made for his game, and it had the exact camera/movement I wanted. I asked him if he could show me either some code or links to how to do that. 

Started tinkering in Godot again, and finally understood what I did wrong. I was moving my camera to the position where I clicked, but the player only moves to that position in a number of gameticks. Lets say it takes 10 gameticks to move the player to that position, I was moving the camera to position 10, instead of position 1. The player however did. Stupid error, but now that I fixed it, it looks smooth AF! 

YEAH! And even without having someone else's code.

Unreal is very nice, don't get me wrong, but the engine is a beast, and so are blueprints. I'm used to coding, and I don't seem to get the hang of the visual programming of blueprints. And learning C++ is not something I want to do at the moment. So, Godot for now, Unreal for a later project.