AIBU to forgive a friend who shouted at me and my children?

She definitely wanted the day out, which is why she refused to let us out of the car during her outburst. She definitely can't be feeling used as it's mainly me who pays for everything for her. I'm embarrassed to admit, that even after her behaviour and the barking order for petrol (which I don't mind paying), I paid for her ticket to enter the destination. I've always paid for her on days out, even though she has a well paid job. She's never questioned it, and never offered to pay her way. I assumed that it was because she's the driver. I always pay for the petrol for her too, out of courtesy. She's just never barked at me like that or ordered me to do it. Reading that back makes it all sound even worse to me.

This. Your behaviour was always as concerning as your friend’s, OP.

She wrires - It's typical that when we were about to leave, one child couldn't find their socks, and then the other child had to go and get changed after noticing a hole in the back of their trousers. Typical sounds repetitive.

I’ve read the OP again and I still can’t see where it says that she’s continually late. Ah well.

That’s strange that you seem to have read that her children are never ready when in fact she says the opposite?

“This delayed us getting to my friends car by about 6-7 minutes after she'd parked up (honestly it was no longer, and we don't usually do this). “

Nothing much to add. She is a willing participant in all of our outings. She's almost been like an auntie to my children.
She's lovely in public, and her colleagues all think she's wonderful, but I've seen multiple rages. I'm talking about little things she rages over too. Another example is when she was at mine, and she'd left her empty glass on the floor for hours. I wanted to tidy up and asked her politely to pick the glass up. I was told not yet. I asked again, and was told that she'd do it when she wanted to. I told her that I wanted it off of the floor now as I was tidying up, then she just exploded in a rage telling me that I had no right to demean her by repeatedly "demanding" her to pick a glass up. She sat in a sulk for about 10 minutes after that, then announced that she was going home. She still didn't pick her glass up.
I guess stupidly, I always accepted her outbursts because I was never in danger, and it was always over something so ridiculous. I know that it's her, not me.

She definitely wanted the day out, which is why she refused to let us out of the car during her outburst. She definitely can't be feeling used as it's mainly me who pays for everything for her. I'm embarrassed to admit, that even after her behaviour and the barking order for petrol (which I don't mind paying), I paid for her ticket to enter the destination. I've always paid for her on days out, even though she has a well paid job. She's never questioned it, and never offered to pay her way. I assumed that it was because she's the driver. I always pay for the petrol for her too, out of courtesy. She's just never barked at me like that or ordered me to do it. Reading that back makes it all sound even worse to me.

How are you getting that from the fact that she refused to let OP and the kids out of the car because she wanted to go on the day out?

The OP said they don't usually keep the friend waiting.

This implies it happens sometimes.

It would be better for it to never happen, and for this delay to have been a once off.

I also don’t think it’s unreasonable for an adult and two nearly teen children to be ready and waiting if they know the time they are being picked up. Punctuality doesn’t seem to count for anything these days.

Long story short, myself and my almost teenage children were going out with a friend of mine for the day. My friend let us know when she had parked outside, and we were to leave our house and go to her car (as she wanted to go straight away and not come inside). It's typical that when we were about to leave, one child couldn't find their socks, and then the other child had to go and get changed after noticing a hole in the back of their trousers. This delayed us getting to my friends car by about 6-7 minutes after she'd parked up (honestly it was no longer, and we don't usually do this). I realise that waiting is a pain in the arse, but I assumed that an apology from me would cut it.
Anyway, when we got into the car, she was very off with me and the children. She then started ranting and droning on about how we take the piss for making her wait. I apologised, but was told that my apology was not accepted as "you know I don't like waiting for anyone".
She literally ranted on and on for around 15minutes non stop. It was making the atmosphere in the car really awkward and uncomfortable, and she was starting to get louder and louder. I apologised again and asked how much longer she was going to go on about it? This enraged her further, and I was met with full on shouting, F bombs, and her fist banging the door on her side, and the steering wheel. This carried on for another 10 or so minutes, continuous expletives and shouting. Myself and my children sat in silence/shock. I then asked her to pull over and let us out of the car, but was refused as she still wanted to go on our day out because I'd apparently already wasted enough of her time.
We spent the rest of the journey in awkward silence, until I was barked at to get out at the petrol station to buy her petrol. I'm not usually a push over, but was so in shock that I did what I was told.
We had a crap time once we arrived at the destination, as she was still raging and making snarky comments.
Once home, I ignored her for a week, until she called to apologise. Then she said it's best we stop talking altogether because her rage was always taking over and she didn't want to keep upsetting me and my children. She has form for this, but I've always stood by her as I've known her and been close to her for years, long before I'd ever seen her rage. These rages are always over trivial things that other people wouldn't bother about.
AIBU if I forgive her?
Sould I just let her go?
Friends are hard to come by, and I've not got any others currently.

You need to step back from this woman, she is dangerous. In the car - "her fist banging the door on her side, and the steering wheel" - she was not fully in control of the car, never mind herself. She could not possibly have been concentrating on the road. She could have crashed and killed you all.

I think your long association with this woman has desensitised you to just how bad she is. Frankly, you're minimising her behaviour.

So yes, you would be unreasonable to forgive her, and totally unreasonable to expose your children to her behaviour again. Do not teach your children to accept being treated like this.

Ditch her. Tell her that her rages are NEVER justified and she needs to get help, and you don't want her around you or your children ever again. Accept no apology, she won't mean it. Remember - "She doesn't see the problem", so she's never going to change.

I’ve read the OP again and I still can’t see where it says that she’s continually late. Ah well.