So angry what is wrong with some parents

At 14, DD should have phoned you asking to be collected. You were relying on her to phone with any emergency, given that you and her mum hadn't swapped numbers.

14 yr olds are not known for good sense.
This was the responsibility of the mum of her friend.

I still can't work out how the OP thought the other mum could get in touch with her as she's currently scrolling FB to find her! You can't physically stop a 14 year old from leaving your house, she didn't have any way to contact you and your daughter was perfectly capable of phoning you herself - and should have given that she was the only person who knew that she wasn't meant to be out on the streets at that time.

By asking the DD. I would have done that

The point was that the mum couldn't have told OP that her DD had left.
So DD was no longer there to ask about her mum's contact details.

OP needs to think about responsibility here.
Either she thinks the responsibility is with the parents i.e. her and the other mum, in which case they should have each other's contact details and some discussion about expectations.
Or she trusts her DD to act responsibly and ring if necessary.

She is complaining that the other mum didn't prevent her DD from leaving the house. I have no idea how the other mum would actually do that. If DD didn't even want to wait outside while she waited 2 minutes for her mum to come, she was hardly going to want to stay in the house after an argument with her friend.
And then there is no way for the other mum to contact her to tell her that DD has gone.

Oh, I can easily stop a 14 yr old leaving the house for the few seconds it takes to get a number. And I would.

"DD had an argument with a friend at a sleepover and was told to get out the house. On her way out the friend's parent stopped her and demanded that DD gave her her mum's phone number. DD just wanted to get out and refused. The other mum then physically stopped her from leaving and kept insisting that she unlocked her phone and gave her the number."

Really?

What's the time limit for something bad to happen to a child alone in the dark? Predators are opportunistic.

They also operate in the light.

So what is winter when it can be dark at 6pm?

This is extreme.
I find it hard to believe the sleepover mum- or me- cannot persuade a 14 yr old to stay in the house for 30 secs longer without laying hands on her or locking her up. It's not Jeremy Kyle. We don't have to be rolling around on the floor. Or revealing state secrets.

I'd be interested to read the other mum's side of this story... OP only has it from her own 14yo, those renowned paragons of truth 😂

Very interested to know her response. If she knew she should have gone after your dd. I certainly would have.

You're just perpetuating the drama by messaging the other mum and it will achieve nothing positive.

Your dd should have called you; just have a chat with her about ding that next time.

So your dds friend kicked her out of the the house at 10pm and her mum allowed it?! I wouldn't let her stay there ever again and honestly I think the other mum is really irresponsible. She should have either phoned you or insisted that your dd sleeps on the sofa. Can't believe she allowed her own DD to kick someone's kid out at 10pm! A 14 year old is a child and vulnerable. I wouldn't turn a 14 year old out on the street, and I'd be alarmed if they had stormed out of the house. She had no idea if your dd was upset and was going to go home or somewhere else.

How long does it take for something bad to happen exactly? 11 mins? I am grown woman and still feel uncomfortable walking alone when it's dark/Id avoid it altogether. You sound woefully naive to the dangers of lone girls and women, at anytime frankly, let alone at night.

Id also add, to everyone blaming the 14 year old for not calling mum, yeah obviously she should have done but she was probably upset, that plus teenage puberty years, - she's still a child with a load of hormones and upset and full of stress and adrenaline from the argument, children don't always make grown up decisions do they, that's why adults are responsible for them until they're 18. The other mum should have been the injection of adult that was clearly needed.

Teenagers are not going to give you a phone number if they don't want to.
An emotional teenager who just wants to get away is even less likely to.

If you try sympathetically you might end up with something like

Other mum: Are you ok? I heard you and friend having an argument?
DD: Friend doesn't want me to stay; I'm going to go home
Other mum: OK, but it's late. Why don't you call your mum from the lounge and wait there until she gets here?
DD: I just want to go
Other mum: It's not really safe to be going home on your own at this time. I'd feel much better to know your mum is on the way.
DD: I'll ring her from outside
Other mum: Can you give me her phone number so I can check you're home safely
DD: <refuses>
Other mum: OK, but please promise me you'll call your mum straight away and wait outside until she gets here
DD: <shrugs and leaves>

This is why it's so important to have the "what if" conversations before hand and then the "was that the best idea" conversations afterwards.

Change the scenario slightly - the girls have gone to McDonalds together (say 7 or 8 in the evening). The plan is for an adult to pick them up later. They have a row and end up separated and not in McDonalds. What do they do? No adult here to pick up the pieces. They have to be able to cope.

Glad you Dd is home safe.
I wouldn't have let that happen if I were the friend's parent. I often walked Dd friends home after dark when she was that age and we live in a relatively safe area.
However, I guess I could have missed what was happening, and my own Dd was always a 'stormer off' including from school once or twice, which led to a 3 mile long unlit cross country walk home and worried me sick.

Usually she called me though, and we had a deal that I would always pick her up from anywhere with no questions, and no reprisal afterwards so long as she trusted me enough to ring. I know this isn't ideal for you (and it wasn't for me either) but it worked.

I would cut your dd some slack. It's embarassing for a teen to leave a sleepover like that, even just telling her parents would be hard.

This sounds realistic

The teens I hung out with appear to be completely different and would have listened to me out of politeness, even if not to their own mums.

Not necessarily. Weirdos, predators, and perverts are everywhere, even the nicer, more middle-class areas. Do not drop your guard and assume you're safe. Always be cautious. The Gift Of Fear. Have you ever heard of it?