I don't understand why your sister inherited the tenancy. Was she a joint-tenant with your mum? If not, (and I doubt she was!) it could be that your mum has left and just not told the council, and your sister is living there and using it as her home. (With it still in your mum's name.)
Having worked in social housing for some years - I don't now but did til 7-8 years ago - I saw this happen a number of times.
ALSO... There is no way a young woman - even with a boyfriend - would be allowed a 2 bed house.
And I don't know any council/social housing landlord who would allow someone to 'inherit the tenancy...' (NOT if she was not a co-tenant - and if she was a child living with mum - then she would not be...) I bet your sister was never on your mum's tenancy.
Something is very off about all this. I would be contacting the council and having them investigate this to be honest. Was she even on the housing list??? If she has taken over this property, it sounds like she has deprived a family of the home, without a) deserving it, and b) being on the housing list.
I know all councils are different, but I would be reporting this to them. If she HAS genuinely been allowed to take over the tenancy, then fine. But I am willing to bet it's not authentic.
Also @Buddybud YANBU to be pissed off and bitter if this HAS happened and she HAS got the tenancy.