Getting the direction a bullet should shoot in

Ello!

So, I am currently making a top down shooter game but I am stuck on how I should shoot the gun.
Right now I know of only 2 options both have their downsides unfortunately.

Option 1 is that I get the mouse position of where I click then send the bullet there, the problem with this is that the bullet looks strange since it can come out of the gun at the wrong angle

Option 2 is that when I click I send the bullet in the direction that the player is facing, the problem with that is that it always goes the the side of where the mouse is

Video of Option 2: (Take notice of how the bullet goes left of where my mouse is)

any information on other methods or the way you do it is appreciated!

change the pivot point of the gun so the barrel rotates around it and lines up with the mouse.

edit: like this, make it rotate around the red dot
image