Severe disability premium - any chance of getting it if brother lives with me?

As I understand it, I am not eligible for Severe Disability Premium because my brother lives in the same house as me and does not meet any of the criteria to be discounted (my mum lives here too, it's her house, but she gets PIP daily living).
What I want to know is, is there any chance of getting SDP if I applied? I feel like my brother shouldn't count because he does not work or contribute anything to the household and we're essentially estranged – him being here does not help me in the slightest.
The other thing is, my mother has asked me to move out and I'm going through the process of applying to go on the housing register – but I can only move into supported housing, and it could be a long wait. Will that be taken into account?
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It seems like such an unfair rule.