So don't give up your lay-up drills against pressure, simply work on getting your players to lock their eyes on the target and keep them there. This is a very common problem for post players as well. Catch, pivot, great post move, and nickel shot because the defender or the ball attracts their eyes from the target. Believe it or not this also is often a common problem with free throw shooting of young players who don't fixate on the target before shooting. Imagine an archer or golfer trying to be accurate while swaying their head off and on the target.
Basketball is certainly no different.
The drill is called the Daily Dozen . They are also practicing ball control when shooting in tight quarters. Many shots near the basket are contested by not only one defender but also often a second or third coming into the play late. This shot will almost be one that hasn't been practice with confidence unless you have practiced the daily dozen. You might even throw in a toss-back machine to make the players pass to themselves.