Council Tax liability on 2 properties

Hi wonder if you can help me out with a slightly complicated case….

Situation is as follows: Cl is a homeowner but has been moved to a council property due to domestic violence - house is on market but not selling.
Cl in receipt of Income Support as lone parent and HB and CTB at council property. She is paying small mortgage of £30.00 a month at home she owns (which is empty at present) and also service charges arrears of Council Tax (and current liability) totalling £96.00 a month and ground rent of £10.00 a month.
The query is: would her brother be able to move in (he claims IB JSA) and claim CTB on this property or would it be better for her to claim CTB on both properties? Also in her situation would it be possible for her to claim DHPs (if she were to claim CTB at the mortgaged property) towards the arrears?
Any suggestions gratefully received -

Thanks

She can’t claim CTB on the owned house, CTB is strictly about the property that you are liable for AND resident in.  There’s no “dual home” provision for CTB as there is with HB.  I’m assumiong she’s had 6 months exemption for the property being vacant/unfurnished & this has now come to an end. 

Her brother could claim CTB as a resident even if he couldn’t claim HB, which would be a whole other set of questions I’m not even going to try & answer.

I may be wrong, but I don’t think she could get DHP for the arrears, above comments aside, as DHPs only take people up to the current liability, not any additions for arrears (I’ve only really seen this with rent in the past, but I can’t see why DHPs for council tax would be any more generous)