A human can definitely make mistakes but mistakes have consequences - unfortunately yours was a BIG mistake. You both husband and wife are born and brought up in India and how easily you forgot the rules of your own country.
You and your wife took your Indian passports and GCs with you. Took your kids' US passports - so you took everything that is needed to get BACK into USA - but you forgot how US citizens enter into a foreign country. How convinient?
Is this arrogance or ignorance on your part? And you expect the immigration offcials to show sympathy for your kids? They just did their duty maybe overzealously but YOU are completely to blame.
The frenchman atleast gets the benefit of doubt coming into India for 1st time. But a person who has lived in that country for 25-30 yrs can forget so easily abt visa? Did you go to US w/o visa and expect the US immigration officials to let you in?
STOP blaming the officials - YOU and your wife are completely at fault - please explain your kids that you made a HUGE mistake and had to face the consequence of that. Its ur responsibility to carry all papers and not of airline to verify - Grow up!
