Please use the direct payments to get the care you need. I know you said your daughter wants to, but she is only young and her life will change. As it rightly should.
Many years ago when I was a student, I'd to choose my courses to fit around carers allowance. It hugely restricted what I could study, and of course studying part time means taking longer to graduate. If she studies the maximum amount of hours allowed to claim carers allowance, she won't be able to take a part time job. So will end up coming graduating with no work experience, and getting passed over for all the other applicants who have experience. The job market is brutal unfortunately.
What happens when she finishes uni and gets offered a place on a graduate scheme? She'd then be going to that job full time. Or is she expected to only work part time in order to continue being your carer? To work part time and still be eligible for Carers Allowance, you're looking at about 16 hours a week on minimum wage. Less hours as your daughter gets older, as the rate of min wage rises. When working part time, she could be rota'd on for a few extra shifts, then benefits will be cut to make up for this.
I was a young carer, back when I started I was happy to do it. I didn't know any better, and I didn't realise how much it would destroy my life. I'm now nearly 40, and still trying to dig myself out of the pit that being a young carer left me in. It destroyed my career, and it's only in the last few years I've managed to get that back on track. Financially due to many years on carers allowance, I'd no savings. And is only the last few years I've been eligible to pay into a company pension.
The isolation of being a young carer. You see the lives of your friends moving on. They're free to travel, socialise, settle down and start their own family. Meanwhile the young carer is being a good little daughter at home helping with the care. It's all well and good til the daughter wakes up and realises her whole life's been wasted, and she's even too old to start her own family.
Please put your daughter's needs first. She's your daughter, not your partner, and should be free to have her own life. Get the outside help you need. Otherwise it'll destroy your relationship. You might think it won't, but back all those years ago when I was about the age your daughter is, my mother would've thought the same.
Also does uni know she's a carer? They probably have some support for carers, eg if she needs someone to talk to or anything.