This is a common problem and it gets asked so much, that the answer should be a sticky.
Since no one has jumped on your question yet, I'll give it a try.
The reason you are hitting low and left, if you are a righty, is due to your grip.
If the grip is too strong, the trigger finger is restricted in motion and the result is a jerking of the trigger with the above mentioned result.
It really doesn't matter if the gun recoils some, as long as it rises and falls straight up and down and the sights land back on the target.
Try lightening up some on the grip, making sure the trigger finger is nice and flexible and see what happens.
When shooting with both hands, the support hand is supposed to provide most of the strength of the grip.
If none of this is clear, check out all the videos on youtube and myoutdooors web sites on the subject.
Lock the doors, they're coming in the windows.