Gosh, I'm really sorry. How frightening.
I hate to say it, but this is pretty standard for crisis teams. They won't come out to you out of hours (ie overnight and at weekends), they'll just tell you to go to A&E. And if you end a call they will not call back.
It's just a person at a desk answering the phone who may or may not be sympathetic if you have worries you want to offload. Their view (which I and pretty much every survivor I've ever spoken to finds appalling) is that if you're calling for help you won't do anything, and you need to take responsibility and take yourself to A&E if it's "really that bad". At most, in some areas, they will call the police on you. Getting your door kicked in and your house searched doesn't tend to have a positive impact on someone in crisis, though.
Even in hours I'm not sure you'd have much luck getting them to come out on the day you call if you don't already have an appointment. It all gets positioned from "you have to take responsibility for yourself" even though the actual problem is their lack of resources and training.
The point of me telling you this is that if you're aware of how they operate you can make informed decisions about what you do next and how to support her.
The complaints process is tough, and your daughter would need support to go through it. Lots of people find it pretty brutal and traumatic. It's possible though that it will result in a review of her care and support so that it better meets her needs. But it also might not change anything at all.
Mind have an info line. I've never used it, but I've heard some people who've found it helpful. It can't hurt to try it as a way of exploring what your options are in terms of care and support going forward. The number is on their website.
Mind also have an online community called Elefriends. Your daughter might find it a place to get support and solidarity from people who relate to what she's going through. It's sort of like Twitter in that it's a continuous feed you post a message on and then people can reply to you with support or advice or "thinking of you" etc type messages - only it's closed and actively moderated and behind screen names not real names, so it doesn't have the abuse and bile of Twitter or other social media and feels safer. Elefriends.org.uk
It might be something that would help her when she's feeling like that as it's instant support, although obviously not a substitute in a full blown crisis, and it does have firm rules so as not to distress or trigger other people. But in the lead up to one or on a bad day or a lonely day... Having a place to talk to other people who've been through it and get it can make a huge difference.
Does she have a care plan or is she under GP care? I'm leaning towards CPA if she's been "privileged" to be granted the crisis team number. (My sarcasm is aimed at them, not you or her). Is it a decent care plan that sets out the steps to follow in a crisis, and what to expect from agencies? Does it detail support for her on a day to day basis to keep her out of crisis? Is it actually helpful?
If not, then trying to get her on the care plan approach with a care coordinator to meet with her on a regular basis and provide practical support seems like a sensible avenue to pursue, although it might take some battling (resources). She would need to be under the care of her local Community Mental Health Team rather than her GP. If she's been ill since she was 12, I'm sort of inferring that she might have been under CAMHS and then graduated to CMHT, so maybe this is already in place? It's possible to be under CMHT but not under CPA with a care plan, so just checking.
If she has a care plan and it's rubbish I'd focus my attention on getting that addressed. If she's not under CMHT/CPA and doesn't have one, I'd be pushing to get that changed. GP managed care hardly seems appropriate.
If she has all of these things, perhaps you could draw up a family crisis plan / care plan? There are templates of the various things covered, but it might be an opportunity to set out the things that will help her cope and avoid a crisis while she's living away from home (finances, activity, leisure time, relationships, physical health, etc etc). Spending some time on building the support structures around her and recognising all the positive things you're already doing but maybe not noticing might help you all feel more in control. It can help to see things written down.
And then a separate crisis plan one for her early warning signs that things are getting worse and how she can respond to them with your involvement maybe? Eg if I wake up feeling like x, then doing y usually helps. / if I start feeling I can't move, then z has helped in the past.
If it could record all the things she has the power to do by herself that are known to help that's great. (Feels less hopeless and powerless when you realise you do all these things to take care of yourself and they do help). It could also set out the ways she can call on your support, and the triggers for you to want her to do that (in the sense of "we don't feel burdened if you contact us because you feel xyz".) and just set out the different options and strategies you can use - Skype, book a coach home for her, go and visit her, pick her up, come and stay at home for the weekend. Etc. So it's written down in an easy to read way and she can see her safety net, and you have the peace of mind that you have a plan.
Obviously only if she's on board and would find this helpful. Or support her to draw up her own more personal version. Even if she has an official care plan sometimes it can feel invasive to share with them all your coping strategies (eg if looking at cute kitten videos online is one of them). Or it might be nice to have a postcard sized version that's easy to take in when she can't focus.
You could set these out in tables (eg for crisis plan: warning signs, things that help, people to contact - in order of severity and escalation). I've also seen crisis plans that are set out with boxes numbered 1 to 10 to match the way you might be asked to grade hoe you're feeling. In each box it describes the warning signs, emotions, reactions, etc and the things that help them.
The advantage of this is that when things are getting bad she can just say "I'm a 5 today" and you know exactly what that means (assuming this is something she wants to do and is ok for you to have a copy) and you can also monitor if she's deteriorating if on Friday she's a 5 but she calls you the next morning saying she's hit 9.
I hope that makes some sense.
Does her uni area have a crisis house or crisis cafe? They can be few and far between but it's worth checking, as they can be a good alternative to A&E when things are getting bad.
My other thought whilst writing, is whether she has a crisis box. Different people use different names - comfort box, anxiety box, etc. Some people use an actual box, some people just have a list of things that serve the purpose and refer to the list to remind themselves what to use.
For instance, it could contain that postcard sized memory jogger of what to do in a crisis. It could have a snuggly blanket she can cuccoon herself in if she's anxious or feeling numb. A candle that smells nice. Photos of people she loves. Photos of favourite places. A note to herself reminding her she can get through this. Little gadgets to fiddle with. The cliched colouring book or art supplies. A little teddy to hug. Those glittery jar things that I have completely forgotten the name of but Johnny Benjamin had one when he did a speech at the RCN(?) conference (glitter jar?!). A favourite book or picture book. Poems. Music or a reminder that playlist abc is often helpful when she feels like this. A note of a particular coping mechanism that is helpful (like holding ice cubes if she feels numb or scrunching paper). If she has preferred strategies like a "body scan meditation" or the 54321 thing or something, she could include a simple instruction sheet to follow when she's struggling to remember it on her own but wants to try them?
Some people make a pretty box to keep all this in, some people have drawstring bags, some of us just have the list somewhere safe and the objects scattered around the house. If she struggles when out and about it can be helpful to have a miniature portable version - eg something comforting that fits in her pocket to hold for reassurance, or a soft scarf she can swaddle herself in and hold onto.
It really depends on what's difficult for her and how she finds it helpful to manage them. I've mainly focused in distress coping ideas here as that's what your posts have been about, but I realise on a day to day basis outside of crisis it might be different issues.
If she's somebody who finds the guided mindfulness "meditations" helpful then she could download a few onto her phone so she can listen to them with earphones anytime she wants, wherever she is. If it's not something she's tried before it can take a bit of getting used to and may not be for her at all (I hated it with a passion at first, found it useful for a while, don't currently use them), so they're not the kind of thing you take up for the first time in crisis, but can help in crisis or to avert crisis once you're used to them.
This website is American, so can be a bit jarring at first, but "soften, soothe, allow" can help when you're in a lot of emotional pain. self-compassion.org/guided-self-compassion-meditations-mp3-2/
Franticworld.com has a bunch of meditations under resources, including a 3 minute one. I've never really been a huge fan of the meditation concept, and like I said hated them at first, but I think when I went through the stage of using them it was because it was helpful to reel like I was being "talked through" how I felt by somebody who didn't require me to talk back and wouldn't be affected if I wasn't paying proper attention.
I'm mentioning these as a possibility for the "distress box" rather than in any expectation it's going to magically cure all her difficulties.
If she wants an understanding person at the end of the phone, samaritans might be a better bet. It's free now which helps, and they can sometimes arrange to call you back to check in with you at a set time the next day if you're really distressed (maybe don't rely on that, as I don't know what makes them decide to offer it, but for you as a parent it might be slightly reassuring to know). Obviously they can't do anything practical, but if the crisis team aren't either... Advantage of samaritans is that if she's not finding the first person she speaks to helpful she can end the call and try again for a different person. Can't do that with crisis team. Only one person on cover OOH usually, so if they're being a compassionless arsehole you're stuck.
I apologise if I'm telling you things you already know, but you sounded (understandably) at your wits end so it seemed better to splurge and let you pick out the things that could be helpful, if anything. I'm just trying to share things that might help manage this over the longer term given than crisis teams can be bloody useless. If it's no use, just scroll past and ignore me (genuinely).
I really hope things start to get better for your daughter. 