The TSA mea not-so-culpa continues:

The screening shown in the video was done in conjunction with a VIPR operation. During VIPR operations, any person entering the impacted area has to be screened. In this case, the Amtrak station was the subject of the VIPR operation so people entering the station were being screened for items on the Amtrak prohibited items list as seen in the video. It should be noted that disembarking passengers did not need to enter the station to claim luggage or get to their car. Signs are posted at the entrance such as the one shown here to the impacted area. Direct Access Point

All persons and property (including vehicles) are subject to search beyond this point. If you elect to enter this area, you may be subject to mandatory screening.

The TSA official explanation, that is, that the dimwitted passengers wandered into a secure area, is contradicted by an explanation from the person who uploaded the video:

There were TSA agents waiting as we got off the train and pointed us to inside and told us to pick up our luggage there. As not being train travelers before, we did what we were told and went inside with the group of people TSA was leading in. Our﻿ luggage was never brought inside. TSA agents were waiting at the door where this sign was (blocked by everyone entering) and as soon as you entered they stepped behind you and would not let you leave and put everyone in a roped off area.

You might want to look at at the video to get an idea of how TSA works outside of an airport. They have created an impromptu corral consisting of station furniture and rope stanchions. Police officers guard the perimeter and entrance to the corral.

The video also shows in detail the search procedure applied to both the mother and the children. Their coats, shoes, and hand luggage are piled on a table, where two Transportation Security Officers ("TSOs") have dumped out their contents and are busy handling and inspecting each item.

The TSO searching the mother has to twice pat down the mother's bra snap. Meanwhile, the TSO is searching the older boy, which includes feeling the boy's arms and legs with both hands, as well as a pat in the area of the boy's belt buckle.

The video ends while the search of the mother is still going on, and the male TSO is moving on to the younger boy. The search of their property is still going on.

Each person searched has had to place their feet on two yellow foot shaped patterns on two black mats and hold their arms outstretched; this allows, in the case of the mother, the TSO to run the metal detection between the mother's legs right up to the mother's crotch.

During the course of the search of the mother, the younger boy, waiting to be searched himself, edges over close to his mother; the mother pushes him away. This seems unusual, but it is likely pursuant to TSA command, as parents are typically ordered to have no physical contact with minor children until both are searched.

Returning to the TSA official version, they do add the following:

However, after looking into it further, we learned that this particular VIPR operation should have ended by the time these folks were coming through the station since no more trains were leaving the station. We apologize for any inconvenience we may have caused for those passengers.