OP, you have to help your dd get DSA. Can you talk her round to agreeing?
It involves filling in DSA forms and then, for my dd, a video call assessment. The DSA assessment was a total walk in the park compared with the PIP assessment. I attended it with my dd.
The DSA assessor just asked dd what her needs were and offered everything on the menu that fit. I believe the cost of equipment, counselling sessions awarded can go up to 20,000 but that may have been a few years ago. The DSA assessor was supportive and made you feel heard, quite the opposite from the PIP assessor who is just looking to trap you into saying the words to deny the claim (i.e. because dd goes to uni, lives on her own, travels to uni on her own), she can do anything and ignore what she said/evidence on her application of her struggling.
Once my dd got DSA, I used the approval letter to support the PIP application. So DSA (easy to get) is a gateway for PIP (hard to get). Of course DSA is only one piece of evidence and not enough for PIP, but it helps to build a picture that is more compelling if your dd has to go before a tribunal. Don't give up before the tribunal. Your dd has to go through the process and get there. Expect to be refused by DWP at Mandatory Reconsideration as that is how they make you lose hope.
Go To The Tribunal. Rinse and repeat.
The tribunal judges are an independent panel and not DWP. DWP is only the other party. DWP will be embarassed by their fuckery being exposed to the tribunal and may even settle before. But you have to make it clear you are very serious and will appeal all the way. Your dd has a 70% chance of success at the tribunal because these 70% have all been screwed by the DWP.
Do not lose hope. I would really recommend you being her PIP appointee. Hopefully your dd will agree. It is a fairly easy process. The assessor comes round to see both you and dd, asks a few questions and that's it. Then as appointee you can take the burden off dd, gather the evidence and do all the paperwork, read up and write the application. As her mother, that is all you want for her, isn't it, to relieve her distress?