Camera Y axis rotation problem

So I’ve been banging my head against the wall with this one. I’ve been doing theese tutorials : https://lwjglgamedev.gitbooks.io/3d-game-development-with-lwjgl/content/chapter8/chapter8.html
and everything works nicely, except camera rotation around vertical (Y) axis. The scene rotates around world origin, which is not intuitive to the user. The camera in this implementation has a position vector (3f) and rotation vector (also 3f) which than make up a view matrix.
My intention is to make camera rotate around the point it is looking at. After a lot of googling and reading I managed to get current camera position in world coordinates (or at least so I belive, the output coords seem correct) by multiplying camera position by inverted view matrix. I calculated point I’d like to rotate it around. I calculated the point where I’d like the camera to be after being rotated, in world coordinates. However when I multiply the resulting point by view matrix (which I assume I should since I got its position by multiplying by inverted view matrix), I get weird values, and when I position camera using those, the problem is not quite resolved as the camera still moves weridly. So my questions are :

  1. How does one correctly position camera at known world coordinates ?
  2. Is this even the correct approach to what I’m trying to accomplish ?