1. As to your situation, there is a very limited possibility of being deselected from Pre-Check eligibility. This can happen randomly or for a reason. Presuming that there is no reason for your deselection, it likely won't ever occur again. Don't give it a second's thought unless you are denied again.

2. As to your kids, depending on their age, they may be able to accompany you through Pre-Check even if they do not qualify for the TTP yet. It goes without saying that once they have GE, they will have Pre-Check.