I think the most important thing, is that your niece is able to concentrate on her current educational stage , now. If she is waiting to do her final 'A' level year, what she needs to be doing now, is resting, to get ready for a new term of work- degrees are important but so is any work she is doing now.
She might not go university at all , if she fails all her exams because she is so distracted by you and her mum arguing down the phone- or through her, by proxy! (Or, she probably would still go, but it would take longer and be a bit more difficult to do )
Then, even in considering university, the most important things for her to look at is- Is it a course she likes? Is it in keeping with her (not your or her mum's even) , but her goals and talents, and does she have a reasonable chance of getting in.
After she's decided what course she wants to do, what she needs to do then is fill in the application forms - and then forget them- because she has her current studying to attend to. Where you live is not part of the application process! She can worry about that when she's got an offer-
When my daughter went to uni, we always knew she would live in halls the 1st year- but we were messing about picking where and which, in the summer holidays before she went, (i.e only weeks before she was due to go) and the university terms don't start till October.
People every year are still getting places, right up to the last minute so it must be possible to decide where you're going to live fairly last minute , too.
Even though it wouldn't be desirable - you could theoretically change where you lived half way through a term-sometimes people have to- the important thing is, to get in somewhere! I don't really understand why she is being pushed -to be making firm accommodation choices, for a university place she doesn't even have yet!
Where she lives isn't a decision that needs to be made now, now, now, I'm not surprised she's feeling she can't face going at all.
I wonder, also, if you don't mind me saying ,if you are being quite fair to her mum. Your niece sounds a good, clever , sweet girl- so I can't help feeling that the woman who brought her up, (alone and in poverty, as well) must have been getting something right! I could't help noticing some things like- you said she's very controlling and doesn't let her daughter do things- but at the same time describe taking your niece off to look round several different universities, ( I felt that was without her mum?). Also, at the beginning,you said her mum had never worked , since her daughter was born, but then later said she does work a few hours a week-so she does work a bit.
Anyway, I hope your niece is able to go to university-where she wants and to be happy and I hope she's able to keep the support of different parts of her family.