I felt like i had some control - although that, of course, is largely an illusion.
We can surprise ourselves.
I used to take tai chi, which our instructor described as "kung fu with the brakes on". Very slow and controlled. One woman in the class was on vacation and actually used a tai chi move automatically to block someone from grabbing her purse. The ironic part is that tai chi is not meant for that - but she did it anyway. She was surprised and amazed that she did this. The body decides to use a well practised move (muscle memory) on its own sometimes.
This is very true, and I think is one of the reasons multiple posters did advise that the kids get martial arts training when ready. It is only one of the range of excellent suggestions in this thread, but like many of them, it's a practiced skill. Having a skill puts you a big step above the untrained.
I was in college with no fight training or useful experience (male, small, skinny; quiet life) when another student attacked me out of the blue. Just grabbed my shirt, shoved me towards the wall and strode off. I had bounced off the wall before I knew what happened. I and the three other students chatting in the hall all looked around for a moment, stunned, after which I retreated into my dorm room, embarrassed. Half an hour later it dawned on me that a button on my shirt had popped off. That was the end of it.
That summer, my younger sister got into martial arts. As a family activity, mom and I joined her. The following year, I joined a Tae Kwon Do class at the college. That was the end of that - until a few years later, moments after I entered a bar, some tall dude grabbed my wrist.
There was a pause for a moment, in which I was amazingly calm because having experience and training; it was a relief compared to the earlier unknown. Then he shoved down, hard, perhaps expecting to push me off balance or toward the floor. By the time I knew he'd done it, I was already three feet back from my original position, but in perfect balance and maintaining the exact same stance I'd had when he shoved me! My body, thanks to balance and movement drills, handled it perfectly - and exactly according to training.
The ensuing moments show how, as you say, a new response comes in the situation. In the background was the training to not pick a fight. I instantly conceived and executed the following: first a slight but growing smile as I studied my opponent, then a slight lean forward to appear desirous of fighting, then a pause as I apparently pulled myself to a stop and wrestled with the temptation to fight. It worked perfectly; after it dawned on the dude that I had not only handled his attack with ease but was confidently ready to fight, he started to sweat. His girlfriend ended the conflict by sweeping in from the side and dragging him away.
I wasn't confident of fighting him; that would be stupid. I had no real intention of fighting, I just pretended. It worked because of the trained reflex, plus the calm that also came from training. I highly support all of the many excellent suggestions in this thread, especially about boundaries, first aid, and martial arts classes. OP, best wishes; I'm sure you'll be (continue being) a fine and caring parent.