It's good that you are considering this, because in my experience pre-ignition push is a much bigger problem in shooters of all levels than trigger discipline. Typically when people try to fight recoil during firing or return the gun to target before it's fired (pre-ignition push), there is a strong low left or right pattern. So, I kind of doubt that's what your issue is. But you can investigate:
Load gun, remove magazine, "shoot" two shots. Only the first shot will be live. The second will be dry. Watch the sights very carefully during both trigger presses.
As @
JCN suggested, it may be as simple as not looking (and aiming) at the same place on the target during each shot. I like 15yds for basic group shooting.
You're not shooting a
Gen1 M&P, are you (sort of joking on this one)?