This reply is not directed to the OP, but to whoever cares to read it.

Please, Please, PLEASE do not operate your lawn mower with your kids in the yard or especially riding along. The situation the OP described happens needlessly several times a year. It is not worth it.

Also, PLEASE NEVER DEFEAT A SAFETY DEVICE ON YOUR LAWNMOWERS!!!

Now, the reason why I am so adamant about lawnmower safety.

Way back when I was 11 years old, I had a horrific lawnmower accident of my own. It was a pushmower, but at the time there was no safety kill switch on the handles of pushmowers.

Anyway, I was mowing in a ditch in my cousin's front yard. Well, little did I know, city workers had came by and dug some of the sand out of the pipe under his driveway and piled it in the ditch. The tall grass hid the little pile of sand. Just enough sand that when I went down and through the bottom, the front of the lawnmower caught on the pile and flipped over.
I tripped and fell on top of the lawnmower and chopped both legs pretty good at thigh level.
I had over 1200 stitches in each leg. One cut was less than 1/2" from my femoral artery.
I am lucky to be here to tell the tale.

I ended up staying in the hospital about a week. The second day, a kid a year or two younger than me came in with his foot chopped off from a lawnmower. It happened just like the story from the OP.

So to sum it up, take lawnmower safety seriously and don't be fricking stupid and ride your kids around or mow with them in the yard.
And for goodness sake, don't tie down the safety bar on push mower handles. It is there for a reason. I wish the one I was using that day would have had one...

BTW, if I see one more dumbass post on here about riding their kids on the mower with the blades engaged, I will post pics of my scars and make you all