AITA for refusing to drive when my nieces and nephew wouldn’t put on their seatbelts and making them late for summercamp?

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The original was posted on /r/AmItheAsshole by /u/Then_Bet_7424 on 2023-07-18 05:41:37.

I (26m) recently drove my nieces and nephew (10f, 8m, 5f) to their summer day camp because my brother had a doctor’s appointment and I was available.

Now, I’m very strict about safety in my car, and I especially don’t tolerate anyone not wearing their seatbelt properly, and that goes double for kids. That day, my nieces and nephew decided to be difficult, and refused to buckle their seatbelts. I refused to start the car until they did, and in the end I had to video call my brother at the doctor’s office waiting room and had him threaten to ground them. We were fifteen minutes late for camp.

After the fact, my brother told me that he was frustrated with me because I “made them late for no reason”. He told me that we rode around in the back of our parents pickup truck all the time and turns out fine (this is true), and that it was a short drive, so it wouldn’t have been a big deal. He said I “have a stick up (my) ass” and need to lighten up a little. That I have no right to discipline his kids, and he just called me a bad guardian in general. He’s probably right that nothing would have happened, but I feel like he’s being too dramatic about fifteen minutes of lateness. AITA?