Hahahahahalol. I did wonder if their giant "NRA Instructor" patches were a little over compensating for something.
Love all you guys posting, there's always some humor to be found.
Sounds like the OP has figured out that the Shield doesn't fit his hand well. I was going to suggest trying several pistol makes at a range that has them available to try.
First, though - neither of your guns are really intended for better accuracy than what you are now getting. They are made for concealment and a few quick shots at close range, for self defense.
A medium to full size pistol will afford much more/better contact with your hands and really tighten up those groups.
A fantastic value these days is the Canik TP9SF
If you are concerned with self defense and not target work or competition, I suggest practicing follow up shots at gradually faster times. Anything in a 10" circle is really good enough for self defense shooting, especially when you shoot "double taps"