Just make a conscious effort to have your strong hand thumb a little further over/away from the slide release. In no time it will be a habit to not have your thumb touching it. I had it happen a couple of times with my Glock just because my thumb is exactly the right length and width to ever-so-slightly touch the slide release, so I just made that adjustment and was good to go.
Sounds like the grip/recoil/trigger problems you have could be a combination of many things. I don't feel like I am experienced enough to give that kind of advice, I will jsut list what is helping me. Someone else can chime in and explain how what I am doing is all wrong. For me its all a mental game, I know the gun is more accurate than me, and capable of whatever the tested X" group at Y yards is.
Here is what I find is helping me:
I would recommend googling 'dave sevigny brian enos combat grip' and reading points 3,4 and 5 here:
http://www.glockfaq.com/content.aspx?ckey=glock_faq_shooting_technique_and_practice
Dry Fire Practice using these tips makes a huge difference for me.
I find concentrating on separating the act of holding the grip from the movement of the trigger finger during dry fire practice helpful. If your grip can stay firm while you move the trigger finger there is much less disturbing your aim. I try to get my trigger finger to act separately from my grip so that I am not tightening my grip to shoot.
For me I repeat 'front sight, front sight....' over and over in my head while making a shot. It keeps me focused on the front sight and not focused on anticipating the shot going off and makes me take my time.
Also when at the range taking every shot one at a time mentally, which results in slow shooting. I was told at first that I shoot too fast. I tried to slow down and found that I was just taking a break and not doing anything but having time pass; the results were the same. After more reading I understand what was really meant by 'too fast'.
The result is that I don't try to shoot slowly, but I try to make sure that I am doing all of these things that are supposed to help me in hopes of one day making it a subconscious habit. The end result is shooting considerably slower without 'trying' to be slow.
YMMV