At Lynch's Fam 1st Family camp in the Seattle area on July 28 ... Lynch had the kids -- some as young as 9 years old -- line up to hit each other without pads.

The exercise got pretty violent, with several kids hitting each other hard ... and throwing each other to the ground.

It appears at some point during the drill, some of the kids had objections toward the workout ... because you can see in the vid, Lynch rounds up about a dozen of them and sent them to run laps.

As we previously reported, according to one of the camp moms, Stephanie Siva, Lynch used curse words while sending the kids to run ... which caused some of them to cry.

In our new video, you can see Siva confronting Lynch about it all on the field ... throwing her son's camp shirt directly at the feet of the former NFL superstar.

Lynch tries to speak with her ... and later, you can see the 32-year-old bolting from the field and sprinting up into the bleachers to try to calm things down with Siva and other outraged parents.

The parents and their kids eventually left the camp ... and in new video we obtained, you can see Lynch grab the mic to address everyone in the crowd over the incident.

"I wanted to say I apologize to the young lady that took off," Lynch said. "She's probably ran off already. But, that is no excuse for what I got going on on this field."

"When they on this field, they belong to me. But, as soon as I'm done, you can have them back. And you can do what you going to do."

Lynch went on to conclude his camp with a sprinting competition ... and it appears the event ended without further incident.

We've reached out to Lynch's camp, but so far, no official comment on the situation.

By the way, we've included the entire, uncut 20-minute video essentially showing the whole camp -- from the drill to the conflict to the apology ... so you can see it all start to finish without edits.

The person who shot the footage (and providing commentary) was a parent who was attending the event and NOT a TMZ staffer.