I have a story about two brothers, they are 14 and 12 and I want the 14 year old to accidentally kill the mother so the other brother will hate him for killing the mother even though it was an accident, any ideas would be appreciated. Thanks.

You didn't say where these people might live; what's the environment? City, suburb, or farm country? There are always sad accidental deaths on farms related to big farm equipment and silos that could have been avoided but because people are tired and just want to get the job do not think about the danger and bad situation they are putting themselves in until it's too late. Or maybe a weather event: flash flood, gets his little brother to safety and tries to grab his mom's hand and can't hold on and she is swept away by raging waters. Snow and ice event that causes death. Personally, i'm tired of hearing about and seeing the accidental death by a gun, but that's always a tried and true option.
Hope one of these ideas inspires a writing spark.

Thank you for your input. It is in the future in the city. I was thinking about a house explosion. The mother and son move the stove for a reason and when they push it back, the gas line cracks and the son goes outside and she lights a cigarette and the house explodes. I was thinking that they could light the pilot light but they wouldn't have to move the stove. Something where the son helps the mom and the brother blames him for what happened.

I was also thinking that the mother has to go to the store because the son needs or wants something and she gets into a car accident and dies. The brother would blame the other brother that it was his fault because if she didn't go to the store for him, she would still be alive. Not sure if they would be in the car with her.

Here are a few ideas that hit my mind.  Hope they help or at least help you think of something you can use.   Good luck with it!

The 14-year-old gets some pills from a schoolmate. Supposed to be ecstasy, but in reality, it's fentanyl.   He comes home and puts them in an empty headache medicine bottle in his room. Mom searches for some medicine for a headache and finds the "headache" pills in her son's room.  She dies from an overdose.

Another one could be he likes to make things from the Anarchist Cookbook. He mixes some chemicals, and it's a dud. So he thinks. Mom finds the bottle, and it explodes when she picks it up.

The 14-year-old wants to poison the neighbor's dog, which terrorizes him.   He grinds up and places poison in some leftovers. He gets distracted.    Mom comes home early and accidentally eats the poisoned food.  

He takes the batteries out of the smoke detectors for one of his electronic devices.   Mom comes homes from the graveyard shift, and he's fixing breakfast for him and his brother.   She goes to bed.  He accidently leaves the stove on, and mom perishes in the fire while they're at school.   The fire department discovers they are no batteries in the detectors.

All three are walking to the store. The 14-year-old and mom get into an argument.  He jerks from her grip, and she loses her balance falling into the roadway in the path of a dump truck.

Wow, you have a lot of good ideas. Thank you very much. Now the hard part of which one. Thank you again.

You could also look at the very creepy and ingenious Six Feet Under TV series openings for inspiration.

I’ll check it out. Thank you very much.

How about the two brothers are shoving each other around playfully while the mother is washing dishes in the sink. They crash into the stove. She yells at them to stop horsing around. She goes to make dinner on the stovetop and it has trouble starting but works eventually. She asks the older brother to look at the stove later and he says he will and the little brother hears this sitting at the table. She asks him to walk his little brother home from school today and he says he will. However, he forgets to do both things. The next time the mother goes to start the stove it explodes from leaking gas as the boys are outside arguing about the one brother forgetting to walk him home.

That’s a good idea too. Thank you very much.