AITAH for yelling at my mother-in-law?

I (33M) was raised in a wealthy but abusive family with extremely controlling parents who dictated what I wore, watched, read, and even ate. I broke out of their house by the time I was 15 and lived semi-independently with friends. My parents always behaved immature, irrational, and reactionary. There was a lot of corporal punishment involved.Once I turned 18 I moved far away and never spoke to them again.

I married my wife (31F) over 7 years ago and we decided to move closer to her family for support. Partly because we knew we won't have a relationship with my parents and partly because we wanted to move to the suburbs.

Everything went smoothly until we had a kid (3yo). Her parents began showing many of the behaviors of my parents and because of the trauma I had endured I could not stand it. I kept telling them both to let me be the parent and not discipline my child or get involved in the decision makings. But her mother specifically, had the same immature, irrational, and reactionary behavior to everything child-related.

She believes we are rookie and terrible parents and only she (a psychiatrist and professor at a prestigious university) has the expertise to raise a child. We are expecting another baby soon and she expects us to let her do the same thing she did with our first. Even though I have had many calm conversations with her about parenting and how joyful it is for me to be in a loving relationship with my child (something I was denied) while also allow my child to be independent, free, and healthy.

A few days ago, during lunch with family, my 3 yo was eating next to my mother-in-law and spilled some food on the ground (we were eating outside). My MIL hysterically scolded my child that it is not okay to spill food because it is hard to clean. I let this one go but my wife (8 month pregnant) did snap back and asked her to stop stressing everyone out.

A bit later, once everyone was done eating, kid was playing outside and fell down 2 or 3 steps. Nothing serious, just a clumsy toddler going down the steps. My MIL immediately jumped out of her seat and began running towards the "dangerous situation" and in that moment, after years of my own helicopter parents' trauma and my MIL’s lack of respect for my parenting style, I snapped and yelled "you are not the parent! Stop acting like one!”
The kid is totally fine, not even a scratch. We grabbed our stuff and left.

Am I the asshole for yelling at her after I have told her numerous times over 3 years not to overstep and intervene in my parenting?