@ItalianPrincess1217 My FIL was horrible to my husbands brother when he would spill something (worse than what you describe, but still I think it’s worth mentioning) and believe me my BIL has not forgotten it. It is part of a pattern of abuse with him, and specifically he was the kid picked on by the father. I don’t know if in the family you are describing has one child being picked on. In most families I don’t think this type of “favoritism” really goes on, even though a lot of children believe they were picked on, but in my husbands family it was objectively true that the father was much much worse towards one child.
Without telling you all the ins and outs, I think maybe he was more accident prone, but that shouldn’t have mattered. I also think he became so nervous about doing something wrong, things kept happening. He definitely has self esteem problem, which turned into being a liar, and stealing (from his parents and credit card companies he left hanging). I can tell you more about it if you want. Again, he was being more than just yelled at, but the message was the kid was a screw up, and his dad was angry.
The parent in question has an anger problem. The one thing to know of everything I know about anger is the person with the problem has “shoulds” in their mind, and tend to have unrealistic expectations. Children “should” behave. My dinner “should” be ready when I come home from work. My niece “should” have invited me to her wedding. All the shoulds are not only expectations, but attached to those things are often hurts. If you can do anything for that parent to learn reasonable expectations of children maybe that will help?
Also, help the children (without making them anxious) to do the right thing before the bad thing happens. My in-laws never made sure the glass was far from the edge of the table, they had expensive breakables displayed on tables practically in the middle of the living room, etc. it was like a set up.
I’m not assuming this parent is some horrible ogre, but he will have some impact on the children I think. Depends on the child how it manifests.