What is the best evidence to support a residential placement for further education (19-25?)

My daughter is 18 and would like to go to university, but this is out of reach as her learning disabilities prevent her from achieving GCSEs let alone A-levels. She is very frustrated and unhappy about being left behind by her peers/ siblings and this causes daily friction at home as she feels - in her own words - 'isolated'. She is very independent in some ways, e.g. having received intensive travel training she navigates London transport easily. However, she is emotionally extremely vulnerable, quite lonely and easily manipulated by anyone who offers friendship. We have already had to step in on two occasions with interventions from CAMHS and her school to prevent this, and can see the seriousness of these incidents escalating as she matures. We are concerned about her safety, her mental health and her ability to progress in education and independence.

We would like her to attend a residential college so that:
- she can make friends who are on her level, whilst learning to distinguish between genuine friendship and exploitation in a safe environment
- she is expected to work full time on practical, vocational skills with the appropriate level of support, repetition and consistency to become truly employable
- she can learn to manage her own finances, laundry, shopping, cooking through a waking day curriculum
We see this as an important stepping stone towards independent living, as she can master new skills but only with intensive training and support.

The local offer would be a part time course within a large mainstream college and she would not be safe there, especially when so much of her week would be unaccounted for while the family is at work and school. There are specialist colleges nearby which would be safer, but only for the 3 days a week that they offer, leaving her at a loose end the rest of the time. In addition, the curriculum at these colleges is very similar to her post-16 'employability' course at her current school, so she wouldn't be progressing much or learning how to work full-time in a practical job, unlike the residential colleges which have indicated that they could meet her needs.

I have asked CAMHS if they can write a letter to support our argument that a residential placement is necessary but they are reluctant to do so, despite having documented one intervention earlier this year which specifically references her 'friend' persuading her to steal on her behalf. Here is what they said: "I have been advised that we have to leave the Local Authority to make the decision without any input from CAMHS. They have explained that they are responsible for the plans, and we only confuse things by getting involved"

Surely we need input from experts close to her, and CAMHS are our only port of call here? My only other entry point is a social care referral and I have made a request but it seems to have gone into a black hole with the local authority.