Outside-in with irons, inside-out with driver

The title pretty much says it all. I hit my irons with a slight pull-fade; it's not anything near a slice, but the divots point a bit left and it's pretty evident that I'm swinging outside-in. What confuses me is that I do the opposite with my driver, 3 wood and hybrid - I have a slight push-draw with them, which is what I'm trying to do with the irons (or at the very least stop cutting across them). I meant to take some videos today, but while I brought my tripod to the range, I forgot to bring the camera... I'll probably have some up up Wednesday or Thursday.

Anyway, it seems that no matter how much I try to swing from the inside with my irons, I still come across the ball, and if I do manage to swing from the inside, I just push the ball way right. I do make good contact pretty consistently, though; I don't catch the ball fat or thin very often at all. I just can't figure out why I hit my driver, 3 wood and hybrid so much better than my irons, and how to go about swinging more inside with my irons. I did try putting a tee behind the ball in a position that would force me to hit from the inside. It did help somewhat, but when I stopped using the tee, I went back to the pull-fade.

I do feel that my weight goes towards the left of the target as opposed to parallel to it, so I sort of end up falling toward my left side. Out of curiosity, though, how does keeping your weight forward promote more of an outward swing path?