In reality, David finished batting (walked), the defense said nothing, and Frank came up and batted. Also, it was the top of the second and not the bottom - my mistake on that.
Here is the best I can recall the conversation between myself and the defensive head coach:
HC: "Hey Chris, I think they just batted out of order."
Me: "Okay, John. Let me see your book."
*I looked at the book, saw the proper order, and asked the runner on first his name, he replied, "Edward." I then asked the batter his name, and he replied, "David."
Me: "John, you're right that they batted out of order, but it's too late to appeal now because you already threw a pitch to another batter and legalized Edward's at-bat."
HC: "Dang. Okay, that's what I thought, but I wanted to make sure. Thanks, Chris."
At this point, no one on the offensive team said or did anything. Remember, this was a rec ball game, I've umpired both these coaches' teams many times over the years, and they know I generally have a reputation for being on top of things.
However, the next time around in the order, before David was supposed to bat in his rightful spot, the offensive manager asked me if they were supposed to follow the order listed in the line-up or the order they had used the first time around - I told him to use the line-up order.