Hi Nora, A "pike" is a short word for "turnpike" and a "turnpike" is an expressway where a toll (fee) is often charged. In North America, some major roads are often referred to as "pikes." However, in this case "further down the pike" is a synonym for "down the road." It's used figuratively here to means "in the future." Dr. Peck is explaining here that in the future these parents will tell themselves that they have done everything possible for their children. Hope this helps! It's a great book :)

This means soon, on in the future. In this case, it's the same as saying "At some point in the future..." This reference to pike refers to a turnpike, which is a type of road. So if you think of your life's journey as a trip along a road, you can appreciate why this makes sense. Some people will say "pipe" instead of pike, but the analogy is similar, and the meaning is the same.